Answer: 99% decrease
Step-by-step explanation: Since the number changes from 6,000 to 60, we know that it's decreasing. Now to find the percent decrease, we divide the amount of change by the original number.
The amount of change is the difference between 6,000 and 60 and the original number is 6,000.
6,000 - 60 is 5,940 so we are left with [tex]\frac{5,940}{6,000}[/tex] and dividing 6,000 into 5,940 gives us 0.99.
Finally, since the problem is asking us for the percent, we write 0.999 as a percent by moving the decimal point 2 places to the right to get 99%.
So when a number changes from 6,000 to 60, it has decreased by 99%.
A section of a hiking trail begins at the coordinates (-7, 5) and follows a straight path that ends at the coordinates (3, 9). What is the rate of change of the hiking trail?
Answer:
The rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].
Step-by-step explanation:
A section of a hiking trail begins at the coordinates (-7, 5). It does mean (x₁, y₁) ⇒ (-7, 5)And follows a straight path that ends at the coordinates (3, 9). It does mean (x₂, y₂) ⇒ (3, 9)In mathematical language, the slope m of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plugging (x₁, y₁) ⇒ (-7, 5) and (x₂, y₂) ⇒ (3, 9) into the slope equation
[tex]m=\frac{9-5}{3-(-7)}[/tex]
[tex]m=\frac{4}{10}[/tex]
[tex]m=\frac{2}{5}[/tex]
So, the rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].
Keywords: rate of change, slope, coordinates
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A new crew of painters can paint a small apartment in 12 hours and experience crew can paint a small apartment in six hours how many hours does it take to paint the apartment on the true cruise work together
Answer:
The new crew and the experience crew working together can paint the apartment in 4 hours.
Step-by-step explanation:
Given:
Time taken by new crew of painters to paint an apartment = 12 hours
Time taken by experience crew of painters to paint an apartment = 6 hours
To find the time taken by them to paint the apartment working together.
Solution:
Using unitary method to determine their 1 hour work.
In 12 hours the new crew can paint = 1 apartment
So,in 1 hours the new crew can paint = [tex]\frac{1}{12}[/tex] of the apartment
In 6 hours the experience crew can paint = 1 apartment
So,in 1 hour the experience crew can paint = [tex]\frac{1}{6}[/tex] of the apartment
Now, the new crew and the experience crew are working together.
So, in 1 hour, they can paint :
⇒ [tex]\frac{1}{12}+\frac{1}{6}[/tex]
Taking LCD = 12, we will add fraction.
⇒ [tex]\frac{1}{12}+\frac{2}{12}[/tex]
⇒ [tex]\frac{3}{12}[/tex]
Simplifying fraction we have:
⇒ [tex]\frac{1}{4}[/tex] of an apartment
Again using unitary method to determine the time taken by them working together to paint the whole apartment.
They can paint [tex]\frac{1}{4}[/tex] of an apartment in 1 hour.
To paint 1 apartment they will take = [tex]\frac{1}{\frac{1}{4}}=4[/tex] hours
Thus, the new crew and the experience crew working together can paint the apartment in 4 hours.
A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as long as it is wide. Both the banner and the poster have perimeters of 24 inches. What are the lengths and wides of the poster and the poster?
Answer:
Length of poster is 9 inches and width of the poster is 3 inches.
Length of banner is 10 inches and width of the banner is 2 inches.
Step-by-step explanation:
Given:
Perimeter of Banner =24 in.
Perimeter of poster = 24 in.
we need to find the dimensions of poster and banner.
First we will find the dimension of poster.
Now Given:
A rectangular poster is 3 times as long as it is wide.
Let the Width of poster be [tex]'p'[/tex].
Length of the poster = [tex]3p[/tex]
Perimeter of poster = 24 in.
But perimeter of poster is equal to twice the sum of length and width.
framing in equation form we get;
[tex]2(p+3p)=24\\\\2(4p)=24\\\\8p=24\\\\p=\frac{24}{8} = 3\ in.[/tex]
Now width of poster = 3 inches
Length of the poster = [tex]3p = 3\times3 =9\ inches[/tex]
Hence Length of poster is 9 inches and width of the poster is 3 inches.
Now we will find the dimension of Banner.
Now Given:
A rectangular banner is 5 times as long as it is wide.
Let the Width of Banner be [tex]'b'[/tex].
Length of the banner = [tex]5b[/tex]
Perimeter of banner = 24 in.
But perimeter of banner is equal to twice the sum of length and width.
framing in equation form we get;
[tex]2(b+5b)=24\\\\2(6b)=24\\\\12b=24\\\\b=\frac{24}{12} = 2\ in.[/tex]
Now width of banner = 2 inches
Length of the banner = [tex]5b = 5\times2 = 10\ inches[/tex]
Hence Length of banner is 10 inches and width of the banner is 2 inches.
The width and length of the rectangular poster are 3 inches and 9 inches, respectively. The width and length of the rectangular banner are 2 inches and 10 inches, respectively. Both were calculated by setting up equations using the perimeter formula for rectangles.
Explanation:The problem is to determine the lengths and widths of a rectangular poster and a rectangular banner, both having the same perimeter of 24 inches. The poster's length is 3 times its width, while the banner's length is 5 times its width. We'll set up two separate equations for their perimeters and solve for the width and length of each.
Poster:Let w be the width of the poster. Then the length is 3w. The perimeter is given by P = 2l + 2w, where P is the perimeter and l is the length. This gives us:
24 = 2(3w) + 2w -> 24 = 6w + 2w -> 24 = 8w -> w = 3 inches
Therefore, the length of the poster is 3w = 9 inches.
Banner:Let x be the width of the banner. Then the length is 5x. Again using the perimeter formula, we get:
24 = 2(5x) + 2x -> 24 = 10x + 2x -> 24 = 12x -> x = 2 inches
Therefore, the length of the banner is 5x = 10 inches.
Cousin Edie drank all of Clark's egg nog.Edie finds a coupon for 50 cents off that can only be use at a local grocery store.Clark normally buys his egg nog at the supermarket. The tax rate at both stores is 2.25% .Which deal is better? Clark:$5:95 plus tax Eddie:6.35+coupon tax
Answer:
Edie has a better deal since his final price is lower
Step-by-step explanation:
Cousin Edie drank all of Clark's egg nog . Edie finds a coupon for 50 cents off that can only be use at a local grocery store.Clark normally buys his egg nog at the supermarket.
The tax rate at both stores is 2.25%.
Clark buys the egg nog at $5.95 plus tax .
Edie buys the egg nog at $6.35 plus coupon plus tax.
After Edie applies the coupon , the final price is $( 6.35 - 0.50 ) = $5.85
Since the percentage of tax applied is the same, the deal with lower final price is better.
Hence, Edie has a better deal.
(3 points)
11. A farmer buys 20 sheep, half male and half female. She was told that the annual rate of
increase for the sheep population is 60%. Assuming that none of the sheep die, when will the
farmer have 200 sheep? Write and solve an exponential equation, showing your work.
Use
to indicate an exponent. Use /to indicate a fraction.
Answer:
The exponential Function is [tex]20+12h=200[/tex].
Farmer will have 200 sheep after 15 years.
Step-by-step explanation:
Given:
Number of sheep bought = 20
Annual Rate of increase in sheep = 60%
We need to find that after how many years the farmer will have 200 sheep.
Let the number of years be 'h'
First we will find the Number of sheep increase in 1 year.
Number of sheep increase in 1 year is equal to Annual Rate of increase in sheep multiplied by Number of sheep bought and then divide by 100.
framing in equation form we get;
Number of sheep increase in 1 year = [tex]\frac{60}{100}\times20 = 12[/tex]
Now we know that the number of years farmer will have 200 sheep can be calculated by Number of sheep bought plus Number of sheep increase in 1 year multiplied by number of years is equal to 200.
Framing in equation form we get;
[tex]20+12h=200[/tex]
The exponential Function is [tex]20+12h=200[/tex].
Subtracting both side by 20 using subtraction property we get;
[tex]20+12h-20=200-20\\\\12h=180[/tex]
Now Dividing both side by 12 using Division property we get;
[tex]\frac{12h}{12} = \frac{180}{12}\\\\h =15[/tex]
Hence Farmer will have 200 sheep after 15 years.
Simplify the cubed root of six over the fourth root of six
six raised to the one twelfth power
six raised to the one fourth power
six raised to the four thirds power
six raised to the seven twelfths power
Answer:
six raised to the one twelfth power
Step-by-step explanation:
The cubed root of 6/the fourth root of 6 equals (6^1/3)/(6^1/4)
6^((1/3)-(1/4))
6^((4-3)/12)
6^1/12
The simplified form of the expression is six raised to the one twelfth power
Given the expression
[tex]\dfrac{\sqrt[3]{6} }{\sqrt[4]{6} }[/tex]According to indices, this expression can also be written as:
[tex]\dfrac{(6)^{1/3}}{6^{1/4}}[/tex]Using the law of indices;
[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]
Applying this expression will give:
[tex]=\dfrac{6^{1/3}}{6^{1/4}} \\= 6^{1/3-1/4}\\=6^{4-3/12}\\=6^{1/12}[/tex]
Hence the simplified form of the expression is six raised to the one twelfth power
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Suppose that $p$ and $q$ are positive numbers for which \[\log_9 p = \log_{12} q = \log_{16} (p + q).\] Then $q/p$ can be expressed in the form $(x + \sqrt{y})/z$, where $x$, $y$, and $z$ are positive integers, and $y$ is not divisible by the square of a prime. Find $x + y + z$.
Value of (x + y + z) = 8
Suppose p and q are the positive numbers for which
[tex]log_(9)p=log_(12)q=log_(16)(p+q)[/tex] from the given expression,
[tex]log_(9)p=log_(12)q[/tex]
[tex](logp)/(log9)=(log(q))/(log12)[/tex]
log(p).log(12) = log(q).log(9)
log(q).2log(3) = log(p).log(12) ------(1)
[tex]Now log_(12)q=log_(16)(p+q)[/tex]
[tex](logq)/(log12)=(log(p+q))/(log(16))[/tex]
log(q).log(16) = log(p + q).log(12)
2log(4).log(q) = log(p + q).log12 -------(2)
By adding both the equations (1) and (2),
2log(3).log(q) + 2log(4).log(q) = log(12).log(p) + log(12).log(p + q)
log(q)[2log(3) + 2log(4)] = log(12)[logp + log(p + q)]
2log(q).log(12) = log(12).log[p.(p + q)]
2log(q) = log[p.(p+q)]
q² = p(p + q)
(q)/(p)=(p+q)/(q)
(q)/(p)=(p)/(q)+1
Let (q)/(p)=a
a = (1)/(a)+1
a² - a - 1 = 0 from quadratic formula,
a = [tex]\frac{1\pm \sqrt{(-1)^(2)-4 \times 1 \times (-1)}}{2}[/tex]
a = [tex](1\pm √((1+4)))/(2)[/tex]
a = [tex](1\pm √((5)))/(2)[/tex]
If the solution is represented by (x+√(y))/(z) then it will be equal to
(1+√((5)))/(2) then x = 1, y = 5 and z = 2.
Now we have to find the value of (x + y + z).
By placing the values of x, y and z,
(x + y + z) = (1 + 5 + 2) = 8
Therefore, value of (x + y + z) = 8
Seattle star blends whole bean coffee worth $3.00 per pound to get 25 pounds of a coffee blend worth $3.50 per pound. How many pounds of both blends does she use?
Answer:
Blend of Whole bean coffee used = 22.5 Ib
Blend of Half bean Coffee used = 2.5 lb
Correction in statement:
The problem statement is missing information. The proper statement is as follows:
Seattle Star blends whole bean coffee worth $3 per pound with half bean coffee worth $3.5 per pound to get 25 pounds of a coffee blend worth $3.05 per pound. How many pounds of each type of coffee does she use?
Step-by-step explanation:
Whole Bean Coffee = $3
Half Bean Coffee = $ 3.5
Amount of whole bean coffee in Pounds (lbs) = Y
Mixture amount of whole bean and half bean blend = 25 lbs
Amount of half bean coffee = 25-Y (lbs)
Total blended mixture = $3.05
Cost of mixture = Cost of whole bean coffee used + Cost of half bean coffee used
3.05 (25) = 3Y + 3.5 (25-Y)
76.25 = 3Y + 87.5 - 3.5 Y
76.25 - 87.5 = 3Y - 3.5Y
- 11.25 = - 0.5 Y
or
0.5 Y = 11.25
Y=[tex]\frac{11.25}{0.5}[/tex]
Y= 22.5 lb
Which is the amount of whole bean coffee.
Amount of half bean coffee = 25-Y = 25- 22.5 = 2.5 lb
So,
Blend of Whole bean coffee used = 22.5 lb
Blend of Half bean Coffee used = 2.5 lb
Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What percentage did sales increase last year? What percentage did sales decrease this year? Sales increased last year, from $5,000 to $10,000. When sales dropped from $10,000 to $5,000 this year, sales decreased .
Answer:
Step-by-step explanation:
Last year, sales at a book store increased from $5,000 to $10,000. The amount by which it increased would be 10000 - 5000 = $5000
The percentage by which the sales increased would be
5000/5000 × 100 = 100%
This year, sales decreased to $5,000 from $10,000.The amount by which it decreased would be 5000 - 10000 = - $5000
The percentage by which the sales increased would be
5000/10000 × 100 = 50%
A woman standing on a cliff is watching a motor boat though a telescope as the boat approaches the shoreline directly below her. If the telescope is 250 feet above the water and if the boat is approaching at 20 feet per second, at what rate is the angle of the telescope changing when the boat is 250 feet from shore
Answer:
Dα/dt = 0.079 degree/sec
Step-by-step explanation:
From problem statement, is easy to see, that if point A is ubicated at the top of the telescope, the shoreline is directly below the woman ( point B), and the point where the boat is, which is at distance x from shoreline is point C. These three point shape a right triangle with angle α (the angle of the telescope).
So we have
tan α = x/250
Differentiating both sides of the equation we get
D (tan α)/dt = ( 1/250)* Dx/dt
sec² α Dα/dt = ( 1/250)* Dx/dt
we already know that Dx/dt = 20 feet/sec
sec² α Dα/dt = 20/250 ⇒ sec² α Dα/dt = 0.08
Dα/dt = 0.08 / sec² α
Then
tan α = 20/250 = 0,08 α = arctan 0.08 α ≈ 5⁰
Dα/dt = 0.08/ sec² α
From tables we get cos 5⁰ = 0.9961 then
1/ 0.9961 = 1.003
sec α = 1.003 and sec² α = 1.0078
Dα/dt = 0.08/ sec² α ⇒ Dα/dt = 0.08/1.0078
Dα/dt = 0.079 degree/sec
The change of position of the boat results in a change of the angle of the telescope, which can be calculated using related rates. With known factors such as the speed of the boat and its distance from shore, the rate of change of the telescope's angle can be found using the principles of trigonometry and calculus.
Explanation:This question is about related rates in calculus. Related rates describe the relationship between different rates of change that are connected to each other. In this case, the changing position of the boat creates a change in the angle of the telescope.
We know the woman is watching a boat that is approaching a shoreline directly below her at 20 feet per second, and we are asked to find the rate that the angle of the telescope is changing when the boat is 250 feet from shore. Here is a way of visualizing it:
Let D be the distance of the boat from the base of the cliff and θ the angle that the telescope makes with the horizontal. We are given that D(t) decreases at 20 feet per second and that when D(t) = 250, we want to know what is dθ/dt.
By using trigonometry, we can find a relationship between D and θ. Specifically, tan(θ) = 250/D, so by implicit differentiation, (sec^2(θ)) * dθ/dt = -250/D^2 * dD/dt. From the given data, dD/dt = -20 and D = 250, so substitute them into the equation and evaluate θ using the tan–1(1) to obtain dθ/dt.
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Tim Has 480 Pokemon cards in his collection, which he arranges in his album. Each page of his album holds 12 cards. The album has 35 pages. Write an expression that shows how many Pokemon cards Tim Has left after he has filled his album completely?
Answer:
Step-by-step explanation:
Total number of Pokemon cards that Tim has in his collection is 480
He arranges the cards in his album and each page of his album holds 12 cards.
The total number of pages in the album is 35. After he has filled his album completely, the total number of cards that the album would contain would be 35 × 12 = 420
Let x represent the number of Pokemon cards he has left. Therefore, the expression becomes
x + 420 = 480
x = 480 - 420 = 60
Find angle A in the following triangle.
A. 35.54
B. 35.67
C. 36.24
D. 36.77
Tan(Angle) = Opposite leg / Adjacent leg
Tan(A) = 5/7
A = Arctan(5/7)
A = 35.54 degrees.
Answer:
A. 35.54
Step-by-step explanation:
To find the angle A in the diagram above, we will simply use angle formula, we will check and see which angle formula will be best fit to use.
The formulas are;
SOH CAH TOA
sin Ф = opposite / hypotenuse
cos Ф = adjacent / hypotenuse
tan Ф = opposite / adjacent
Looking at the figure given, since we are to find angle A, then our adjacent is 7 and the opposite is 5.
since we are given both opposite and adjacent, then the best formula to use for this is tan Ф
tan Ф = opposite / adjacent
opposite = 5 and adjacent =7
we will go ahead and insert our values
tan A = 5/7
tan A = 0.71429
To get the value of tan A, we will simply take the [tex]tan^{-1}[/tex] of both-side
[tex]tan^{-1}[/tex] tan A = [tex]tan^{-1}[/tex] 0.71429
A = 35.54
Therefore angle A is 35.54
A residual plot has data points that are all very close to the x-axis. What does this say about the data?
A) The line of best fit will be a horizontal line.
B) A linear model is appropriate.
C) There is not enough information to determine this.
D) A non-linear model is appropriate.
Answer:
B
Step-by-step explanation:
because, the closer the data points are to the x axis on a residual plot with no definite shape means that a linear model is appropriate for this data set
A linear model is appropriate because, the closer the data points are to the x axis on a residual plot with no definite shape. So, option B is correct.
What is residual plot?A residual is a measure of how far away a point is vertically from the regression line.
It is the error between a predicted value and the observed actual value.
A residual plot is a graph that has data points that are all very close to the x-axis. It shows the residuals on the y axis and the independent variable on the x axis.
The goodness of fit of a linear model is depicted by the pattern of the graph of a residual plot. If each individual residual is independent of each other, they create a random pattern together.
When graphing the residual values you know if a linear model is an appropriate model for your data if the points in the residual plot are scattered.
A linear model is appropriate because, the closer the data points are to the x axis on a residual plot with no definite shape.
So, option B is correct.
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Solve the system of equations: (Find the ordered pair that is a solution to both equations). y=4x-3y=-2x+9
Answer:
(-2,-11)
Step-by-step explanation:
x = -2
y = -11
The envelop weighs 1/2 of the whole balloon The weight of the basket is 3/5 of the envelope if the weight of the balloon will be 210 kg what is the weight of the basket
Given the total weight of the hot air balloon as 210 kg, the envelope weighting half of this, the weight of the basket, which is 3/5 of the envelope, is calculated to be 63 kg.
To determine the weight of the basket attached to a hot air balloon, we can use the information that the envelope weighs [tex]\frac{1}{2}[/tex] of the total weight of the balloon and that the basket weighs [tex]\frac{3}{5}[/tex] of the envelope's weight. If the total weight of the hot air balloon will be 210 kg, then the envelope weighs 105 kg (which is [tex]\frac{1}{2}[/tex] of 210 kg). The weight of the basket can then be calculated as:
Weight of the balloon = 210 kg
Weight of the envelope = 210 * (1/2) = 105 kg
Weight of the basket = 105 * (3/5) = 63 kg
Therefore, the weight of the basket is 63 kg.
Alexander and Jo live 5 miles apart. They decide to leave their homes at 3 p.M. And travel toward each other. If Alexander bikes 14 miles per hour and Jo jogs 6 miles per hour, when will they meet?
Answer:
Step-by-step explanation:
Here is an illustration of the problem:
----------------------------->|<------------------
A t J
Alex and Jo start from their separate homes and drive towards one another. The t indicates the time at which they meet, which is the same time for both. Filling in a d = rt table:
d = r x t
Alex 14 t
Jo 6 t
The formula for motion is d = rt, so that means that Alex's distance is 14t and Jo's distance is 6t.
14t 6t
---------------------------------->|<------------------
A t J
The distance between them is 5 miles, so that means that Alex's distance plus Jo's distance equals 5 miles. In equation form:
14t + 6t = 5 and
20t = 5 so
t = .25 hours or 15 minutes.
If they leave their homes at 3 and they meet 15 minutes later, then they meet at 3:15.
A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by A(t) = 10(0.7)t and that in order for the drug to be effective, at least 4 milligrams must be in the body.
a. Determine when 2 milligrams is left in the body.
b. What is the half-life of the drug?
Answer: a - 4.512 hours
b - 1.94 hours
Step-by-step explanation:
Given,
a) A(t) = 10 (0.7)^t
To determine when 2mg is left in the body
We would have,
A(t) = 2, therefore
2 = 10(0.7)^t
0.7^t =2÷10
0.7^t = 0.2
Take the log of both sides,
Log (0.7)^t = log 0.2
t log 0.7 = log 0.2
t = log 0.2/ 0.7
t = 4.512 hours
Thus it will take 4.512 hours for 2mg to be left in the body.
b) Half life
Let A(t) = 1/2 A(0)
Thus,
1/2 A(0) = A(0)0.7^t
Divide both sides by A(0)
1/2 = 0.7^t
0.7^t = 0.5
Take log of both sides
Log 0.7^t = log 0.5
t log 0.7 = log 0.5
t = log 0.5/log 0.7
t = 1.94 hours
Therefore, the half life of the drug is 1.94 hours
If a borrower's monthly interest payment on an interest-only loan at an annual interest rate of 7.3% is $877, how much was the loan amount (rounded to the nearest hundred)?A. $120,100B. $100,300C. $144,200D. $134,200
Answer:
C. $144,200
Step-by-step explanation:
We have been given that a borrower's monthly interest payment on an interest-only loan at an annual interest rate of 7.3% is $877.
To find the loan amount, we will use simple interest formula.
[tex]I=Prt[/tex], where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
One month will be equal to 1/12 year.
[tex]7.3\%=\frac{7.3}{100}=0.073[/tex]
Upon substituting our given values in simple interest formula, we will get:
[tex]877=P*0.073*\frac{1}{12}[/tex]
[tex]877*12=P*0.073*\frac{1}{12}*12[/tex]
[tex]10524=P*0.073[/tex]
[tex]P*0.073=10524[/tex]
[tex]\frac{P*0.073}{0.073}=\frac{10524}{0.073}[/tex]
[tex]P=144164.3835616438356[/tex]
Upon rounding to nearest hundred, we will get:
[tex]P\approx 144,200[/tex]
Therefore, the loan amount was $144,200 and option C is the correct choice.
Final answer:
To calculate the loan amount based on a monthly interest payment and an annual interest rate, convert the rate to monthly and divide the payment by this rate. For a monthly payment of $877 at 7.3% annual interest, the loan amount is approximately $144,200.
Explanation:
To determine the loan amount of an interest-only loan given a monthly interest payment and an annual interest rate, follow these steps:
Convert the annual interest rate to a monthly rate by dividing by 12.Divide the monthly interest payment by the monthly interest rate to find the loan principal.In this case, the annual interest rate is 7.3%, so the monthly interest rate is 7.3% / 12 = 0.6083%. The monthly interest payment is $877. Therefore, the loan amount can be calculated as follows:
$877 / 0.6083% = $877 / 0.006083 = $144,200.46
When rounded to the nearest hundred, the loan amount is $144,200.
The correct answer is C. $144,200.
Mario's Pizza just recieved two big orders from customers throwing parties. The first customer, Hugo, bought 7 regular pizzas and 1 deluxe pizza and paid $74. The second customer, Vincent, ordered 5 regular pizzas and 1 deluxe pizza, paying a totsl of $58. What is the price of each pizza?
The price of each regular pizza is $8 and the price of each deluxe pizza is $10.
Explanation:To find the price of each pizza, we need to set up a system of equations using the given information. Let's denote the price of a regular pizza as 'r' and the price of a deluxe pizza as 'd'. Using the first customer's order, we can write the equation: 7r + d = 74. Using the second customer's order, we can write the equation: 5r + d = 58. To solve this system of equations, we can subtract the second equation from the first equation to eliminate the 'd' variable: (7r + d) - (5r + d) = 74 - 58. Simplifying, we get 2r = 16, which gives us r = 8. Plugging this value back into the first equation, we find d = 10. Therefore, the price of each regular pizza is $8 and the price of each deluxe pizza is $10.
If natalie and her friends decide to rent 4 lanes at reguler cost for a party ten people need to rent shoes and 4 people are members what is the total cost for the party
The question is missing a tabular data. So, it is attached below.
Answer:
The total cost for the party is $74.50.
Step-by-step explanation:
Given:
Lanes rented at regular cost = 4
Cost of 1 lane rented at regular cost = $9.75
Cost of 1 lane rented for members = $7.50
Cost of 1 shoe rental at regular cost(non members) = $3.95
Cost of 1 shoe rental for members = $2.95
Since, lanes are rented at regular cost, we use unit rate at regular cost
So, cost of 4 lanes rented = [tex]4\times 9.75= \$ 39[/tex]
Now, out of 10 people who rented shoes, 4 are members. So, the number of non-members is given as:
Non members who rented shoes = 10 - 4 = 6
So, 4 members and 6 nonmembers rented shoes.
So, cost of 6 non members renting shoes = [tex]6\times 3.95=\$ 23.70[/tex]
Cost of 4 members renting shoes = [tex]4\times 2.95=\$ 11.80[/tex]
Total cost for the party is the sum of all the costs. This gives,
= 39 + 11.80 + 23.70
= 50.80 + 23.70
= $74.50
Therefore, the total cost for the party is $74.50.
Simon has 20 quarters and 12 dimes.He wants to purchase ice cream for his friends.An ice cream cone cost $1.00.How many cones can Simon buy for his friends?
Answer:
6
Step-by-step explanation:
Each ice cream cone costs 4 quarters or 10 dimes, so Simon has ...
20/4 + 12/10 = 5 + 1.2 = 6.2
times the price of an ice cream cone. He can buy 6 cones for his friends.
PLEASE HELP
which graph represents the given inequality y < 3x-4
Answer: Here is the answer.
Step-by-step explanation:
PLEASE HELP
CD¯ has endpoints C and D, with C at coordinates (5,8). CD¯- has midpoint M at (3,9).
What are the coordinates of point D?
Answer:
(1, 10)
Step-by-step explanation:
Use midpoint formula.
Mₓ = (x₁ + x₂) / 2
3 = (5 + x) / 2
6 = 5 + x
x = 1
Mᵧ = (y₁ + y₂) / 2
9 = (8 + y) / 2
18 = 8 + y
y = 10
The coordinates of point D are (1, 10).
The coordinates of point D are (1, 10).
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something.
Midpoint of a line segment means a point which lies in the mid of the given line segment.
Given; CD has endpoints C and D, with C at coordinates (5,8). CD has midpoint M at (3,9).
Using midpoint formula;
Mₓ = (x₁ + x₂) / 2
3 = (5 + x) / 2
6 = 5 + x
x = 1
Now, Mᵧ = (y₁ + y₂) / 2
9 = (8 + y) / 2
18 = 8 + y
y = 10
Hence, The coordinates of point D are (1, 10).
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When Justin goes to work, he drives at an average speed of 65 miles per hour. It takes about 1 hour and 30 minutes for Justin to arrive at work. His car travels about 25 miles per gallon of gas. If gas costs $3.65 per gallon, how much money does Justin spend on gas to travel to work?
Answer:
Justin spends $14.24 on gas to travel to work.
Step-by-step explanation:
Given:
Average speed at which Justin goes to work = 65 miles/hour
Time taken by Justin to arrive at work = 1 hour and 30 minutes = 1.5 hours [As 30 minutes =0.5 hours]
Distance he can travel per gallon of gas = 25 miles.
Cost of per gallon of gas = $3.65
Solution:
We first determine the distance Justin travels to work.
Distance = [tex]Speed\times time[/tex]
Distance = [tex]65\times 1.5 = 97.5\ miles[/tex]
Using unitary method to find the amount of gas required to cover the distance.
If 25 miles is covered in 1 gallon of gas
Then 1 mile will be covered in = [tex]\frac{1}{25}[/tex] gallons of gas
So, to cover 97.5 miles gas required = [tex]\frac{1}{25}\times 97.5=3.9[/tex] gallons of gas.
Using unitary method to find the cost of 3.9 gallons of gas.
Cost of 1 gallon of gas = $3.65
So, cost of 3.9 gallons of gas will be = [tex]\$3.65\times 3.9=\$14.235\approx\$14.24[/tex] (Answer)
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?
Answer:
23
Step-by-step explanation:
We can check all the possibilities.
It is not necessary to consider y>16, because in this case, 16#y=16 as 16 is too small to be split in y parts.
Now, 1,2,4, 8 and 16 are factors of 16. When you divide 16 by any of the previous integers, the remainder is zero so we discard these.
When y=3, 16=5(3)+1, 16#3=1 so we add y=3. From this, 16=3(5)+1 thus 16#5=1 and we add y=5.
We discard y=6 as 16#6=4 (using that 16=6(2)+4). We also discard y=7 because 16=2(7)+2 then 16#7=2.
For y=9,10,11,12,13,14, when dividing the quotient is one so 16#y=16-y>1 and these values are discarded. However, we add y=15 because 16=15(1)+1 and 16#15=1.
Adding the y values, the sum is 3+5+15=23.
A garden hose emits 9 quarts of water in 6 seconds at this rate How long will it take the hose to emit 12 quarts how much water does the hose emit in 10 second
Answer:
8 seconds
15 quarts
Step-by-step explanation:
Givens
6 seconds emits 9 quarts of water.
x seconds emits 12 quarts of water.
Formula
6/x = 9/12
Solution
Cross multiply
9x = 12*6 Simplify the right
9x = 72 Divide by 9
9x/9 = 72/9
x = 8 seconds Answer.
In 8 seconds, the hose will emit 12 quarts
=========================
Givens
9 quarts of water are emitted in 6 second
x quarts of water are emitted in 10 seconds
Formula
9/x = 6/10 Cross multiply
Solution
9*10 = 6x Combine the left
90 = 6x Divide by 6
90/6=6x/6
15 = x
In 10 seconds the hose emits 15 quarts.
Answer:
Step-by-step explanation:
The garden hose emits 9 quarts of water in 6 seconds. It means that the number of seconds that it takes the garden hose to emit 1 quart of water would be 6/9 = 2/3 seconds
Therefore, the number of seconds that it will take the garden hose to emit 12 quarts of water would be
12 × 2/3 = 8 seconds.
Again, the number of quarts that the garden hose will emit in one second is 9/6 = 3/2 quarts.
Therefore, the number of quarts of water that the hose emits in 10 seconds would be
10 × 3/2 = 15 quarts.
A quilt is made of 8 rows of squares, and there are 6 squares in each row. Each square measures 1 foot on a side. Explain how to find the area of the quilt in a square feet. Then write the area.
Answer:
48
Step-by-step explanation:
Answer:
Step-by-step explanation:
The total number of rows of squares in the quilt is 8. Each row contains 6 squares.
Since each square measures 1 foot on a side, the area of each square would be 1^2 = 1 foot^2
This means that each row contains six 1 foot^2. Since there are 8 rows, a triangle would be formed such that one of its sides is
6 × 1 foot == 6 feets and the other side would be
8 × 1 foot = 8 feets.
The area of the quilt in a square feet would be the area of the rectangle. It becomes
6 × 8 = 48 feets
If a and b are positive integers such that gcd(a,b)=210, lcm[a,b]=210^3, and a
The problem can be solved by using a theorem from number theory stating that gcd(a, b) * lcm[a, b] = a * b. Applying this theorem with the given values leads us to solution where a = 210^2 and b = 210^2.
Explanation:In this mathematics problem, we're given two positive integers, a and b, whose greatest common divisor (gcd) equals to 210, and the least common multiple (lcm) equals to 210^3.
It is a well-known theorem in number theory that for any two positive integers a and b, gcd(a, b) * lcm[a, b] = a * b. We can apply this theorem to our problem. Since we know the values for greatest common divisor and least common multiple, namely gcd = 210 and lcm = 210^3 = 210 * 210 * 210, we have:
210 * 210^3 = a * b
This can be simplified to a * b = 210^4. Since we're told that a < b, and both a and b must divide 210^4, the only possible values for a and b are a = 210^2 and b = 210^2, which respects the condition a < b.
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A test car went 64 miles on 2 gallons in the morning, 16 miles on 1/2 gallon at noon, and 32 miles on 1 gallon at 5 PM.Is the relationship a proportional relationship? Explain.
It is proportional because the relationship between gallons of gas and distance is constant and linear. The rate is 32 miles per gallon. You can also call 32 the slope of this linear relationship.
When 25 students went to Washington dc 18 of them visited the museum of natural history and 22 visited the natural air and space museum. How many students visited both museums.
Answer:
15 students visited both museums.
Step-by-step explanation:
Operations With Sets
Sets are a collection of elements. Some sets have elements in common with other sets. These elements are said to be in their intersection. If we know the number of elements in the set A and in the set B, and also the total number of elements in both sets, we can say
[tex]N(A\bigcup B)=N(A)+N(B)-N(A\bigcap B)[/tex]
where [tex]N(A\bigcup B)[/tex] is the total number of elements, N(A) and N(B) are the number of elements in A and B respectively, and [tex]N(A\bigcap B)[/tex] is the number of elements in their intersection. If we wanted to know that last number, then we isolate it
[tex]N(A\bigcap B)=N(A)+N(B)-N(A\bigcup B)[/tex]
Let A= Students who visited the museum of natural history
B=Students who visited the natural air and space museum
We know [tex]N(A)=18, N(B)=22, N(A\bigcup B)=25,\ so[/tex]
[tex]N(A\bigcap B)=18+22-25=15[/tex]
Answer: 15 students visited both museums.
Note: We are assuming no students didn't visit at least one museum
The set theory in Mathematics implies that 15 out of the 25 students must have visited both the Museum of Natural History and Natural Air and Space Museum, since these students are counted twice when you add the students who visited each museum separately.
Explanation:The problem asked is: When 25 students went to Washington DC, 18 of them visited the Museum of Natural History and 22 visited the Natural Air and Space Museum. How many students visited both museums?
To answer this, we need to understand the concept of the set theory in Mathematics. It helps us know the total number of students who visited both museums: we subtract the total number of students from the sum of students who visited each museum separately.
So, if we add those who visited the Museum of Natural History (18 students) and those who went to the Natural Air and Space Museum (22 students), we get 40. But we know there were only 25 students in total, implying that 15 students must have visited both museums since these students are counted twice in our sum. Therefore, 15 students visited both museums.
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