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Related Questions
A marathon runner will donate $5000 to charity if her time is less than or equal to 3 hours. She will donate $2000 if her time is more than 3 hours but less than or equal to 4 hours. Finally, she will donate $1000 to charity if her time is more than 4 hours.
a.)Write a piecewise function describing this situation.
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[tex]\bf f(x)= \begin{cases} 5000&t\le 3\\ 2000&3\ \textless \ t\le4\\ 1000&t\ \textgreater \ 4 \end{cases}[/tex]
Write an equation of the line perpendicular to the line 8x+15y=12 and containing the point (11,17) write the answer in standard form
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The slope of a line perpendicular to another line has a slope which is the negative reciprocal of that line or:
m1 = -1/m2
First, we convert the given equation into slope-intercept form of a line: y = mx + b
8x + 15y = 12
15y = -8x + 12
y = (-8/15) x + 0.8
m1 = -8 / 15
Therefore the slope of the perpendicular line is:
m2 = 15 / 8
Since the perpendicular line crosses the point (11, 17), therefore using the slope formula:
m = (y2 – y1) / (x2 – x1)
15 / 8 = (y2 – 17) / (x2 – 11)
1.875 (x2 – 11) = y2 – 17
1.875 x2 – 20.625 = y2 – 17
y2 = 1.875 x2 – 3.625
y = (15/8) x – 3.625
multiplying both sides by 8:
8y = 15x – 29
rewriting in standard form:
15x – 8y = 29 (ANSWER)
Gabrielle's age is two times Mikhail's age. The sum of their ages is 72 . What is Mikhail's age?
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The age of Mikhail's is 24 years old.
To find Mikhail's age, let's denote Mikhail's age as ( x ) and Gabrielle's age as ( 2x ) (since Gabrielle is twice as old as Mikhail). We know the sum of their ages is 72. We can set up an equation to represent this information:
[tex]\[ x + 2x = 72 \][/tex]
Step 1: Combine like terms
Combine the (x) terms on the left side of the equation:
[tex]\[ x + 2x = 3x \][/tex]
So, the equation simplifies to:
[tex]\[ 3x = 72 \][/tex]
Step 2: Solve for ( x )
To find the value of ( x ), divide both sides of the equation by 3:
[tex]\[ x = \frac{72}{3} \][/tex]
[tex]\[ x = 24 \][/tex]
Therefore, Mikhail's age is 24 years old.
Mikhail's age is 24. Gabrielle is 48.
Let's solve it step by step:
1. Let's represent Gabrielle's age as [tex]\( G \)[/tex] and Mikhail's age as [tex]\( M \)[/tex].
2. According to the given information, Gabrielle's age is two times Mikhail's age, so we can express this as an equation:
[tex]\[ G = 2M \][/tex]
3. We also know that the sum of their ages is 72, which can be expressed as another equation:
[tex]\[ G + M = 72 \][/tex]
4. Now, we have a system of two equations:
[tex]\[ G = 2M \][/tex]
[tex]\[ G + M = 72 \][/tex]
5. Substitute the value of [tex]\( G \)[/tex] from the first equation into the second equation:
[tex]\[ 2M + M = 72 \][/tex]
[tex]\[ 3M = 72 \][/tex]
6. Divide both sides by 3 to solve for [tex]\( M \)[/tex]:
[tex]\[ M = \frac{72}{3} \][/tex]
[tex]\[ M = 24 \][/tex]
7. So, Mikhail's age is 24 years.
Now, to verify, we can find Gabrielle's age using the first equation:
[tex]\[ G = 2M \][/tex]
[tex]\[ G = 2(24) \][/tex]
[tex]\[ G = 48 \][/tex]
Gabrielle's age is indeed 48 years.
So, to recap, Mikhail's age is 24 years.
Susan enlarged to scale a rectangle with a height of 4 centimeters and length of 11 centimeters on her computer. The length of the new rectangle is 16.5 centimeters. Find the height of the new rectangle
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4 * 1.5 = 6 cm <== Because this is the answer.
Thomas works as an underwater photographer he starts at a position that is 15 feet below sea level he rises 9 feet then descends 12 feet to take a photo of a coral reef write and evaluate an expression to find his position relative to sea level when he took a photo
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0-15+6-12=18
Effective rate (APY) is: Never related to compound table Interest for one year divided by annual rate Interest for one year divided by principal for 2 years Interest for one year divided by principal None of these
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is the rate we get for depositing an amount for a year after taking into account compound interest.
Therefore it is the interest for one year divided b the principal.
I REALLY NEED HELP PLEASE!!
Mark is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 6 km/h. After three hours, the velocity of the runner is 2 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points) Part B: How can you graph the equations obtained in Part A for the first 5 hours? (5 points)
I really need to finish this today please help!!
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part A)
[tex]\bf \begin{array}{ccllll} hours(x)&velocity(y)\\ -----&-----\\ 1&6\\ 3&2 \end{array}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 6}})\quad % (c,d) &({{ 3}}\quad ,&{{ 2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-6}{3-1}\implies \cfrac{-4}{2}\implies -2[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-6=-2(x-1)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-6=-2x+2\implies y=-2x+2+6\implies \boxed{y=-2x+8}[/tex]
part B)
well, we know y = -2x+8.... so.. what's the runner's velocity after 5hours? well, x = 5, thus y = -2(5) +8 ---> y = -2
to graph it, well, is a LINEar equation, meaning the graph is a LINE, and to graph a line, all you need is two points, and by now, you have more than two.. so graph it away.
What is the third step when factoring the trinomial ax^2+bx+c, after you have factored out a common factor in each term?
a.) Add the linear terms together
b.)Multiply the factors together to check
c.)Factor the simplified trinomial
d.) Distribute the common factor
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After factored out a common factor in each term. Factor the simplified trinomial. Option c) is correct.
Step after the the third step when factoring the trinomial ax^2+bx+c to be determine.
Factors is are the sub multiples of the value.
Here,
After factored out a common factor in each term. The next step come is to factor the simplified term which implies taking common and kept in parenthesis.
Thus, after factored out a common factor in each term. Factor the simplified trinomial.
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Can someone answer this ASAP? I got 52 which as a decimal would be 0.52 but it was wrong. What is the correct answer?
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since cone B is bigger it needs to weigh more than 20 lbs.
5/13 = 20/X
x=52 LBS
Find the slant height of this square pyramid 6 inches on each side
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Ruby is visiting a wildlfe center to gather information for he paper . The center has circular pond with a diameter if 20. What is the approximate area of the pond ?
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area = PI x r^2
r = 20/2 = 10
3.14 x 10^2 = 314 square units
Which of these ordered triples indicates where the plane cuts the x-axis for this equation? 7x +2y +3z =42 A. (14,0,0) B. (7,0,0) C. (21,0,0) or D. (6,0,0)
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Given:
7x +2y +3z =42
I assumed that the format in the given choices is (x,y,z). So, I substituted each number to its corresponding variable.
A. (14,0,0) → 7(14) +2(0) +3(0) = 42 → 98 + 0 + 0 ≠ 42 NOT THE ANSWER
B. (7,0,0) → 7(7) +2(0) +3(0) = 42 → 49 + 0 + 0 ≠ 42 NOT THE ANSWER
C. (21,0,0) → 7(21) +2(0) +3(0) = 42 → 147 + 0 + 0 ≠ 42 NOT THE ANSWER
D. (6,0,0) → 7(6) +2(0) +3(0) = 42 → 42 + 0 + 0 = 42 CORRECT ANSWER.
The ordered triples indicated where the plane cuts the x-axis for this equation is D. (6,0,0).
Answer:
Option D is correct.
Step-by-step explanation:
Given Equation of plane is 7x + 2y + 3z = 42
We need to find ordered triplet where plane cuts the x-axis.
To find point of x-axis when plane cuts it. we put other coordinates equal to 0.
So, put y = 0 and z = 0 in equation plance to get x-coordinate of the required ordered triplet.
7x + 2 × 0 + 3 × 0 = 42
7x + 0 + 0 = 42
7x = 42
[tex]x=\frac{42}{7}[/tex]
x = 6
⇒ ordered triplet = ( 6 , 0 , 0 )
Therefore, Option D is correct.
Divide and state the quotient in simplest form.
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= --------------- * -------------------
(y+1)^2 36y
y (y -1)
= ------------ * ----------
(y+1) 4
y^2 - y
= ----------------
4y + 4
or
y(y - 1)
= ----------------
4(y + 1)
what are the intercepts of the graph (0,7)(9,0)(-9,0)
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Charles can type 675 words in 9 minutes. How many words can Charles types in 13 minutes?
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So, just multiply 75 by 13 minutes and you should get 975 words.
The answer is 975 words in 13 minutes
Addison has 15 fewer pieces of candy than Ronny does. Is this situation modeled by an expression or equation? How do you know?
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Equation, because Addison's candy is equal to 15 less than Ronny's candy.
i hope this help you
Answer:
Equation, because Addison's candy is equal to 15 less than Ronny's candy.
Step-by-step explanation:
Theo started to solve the quadratic equation (x + 2)2 – 9 = –5. He added 9 to both sides and the resulting equation was (x + 2)2 = 4. Next, he took the square root of each side. Which was the resulting equation of that step?
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we have
[tex](x + 2)^{2}-9=-5[/tex]
Adds [tex]9[/tex] both sides
[tex](x + 2)^{2}-9+9=-5+9[/tex]
[tex](x + 2)^{2}=4[/tex]
square root both sides
[tex](x+2)=(+/-)\sqrt{4}\\(x+2)=(+/-)2\\x1=2-2=0 \\x2=-2-2=-4[/tex]
therefore
the answer is
the resulting equation is [tex](x+2)=(+/-)2[/tex]
Answer: [tex](x+2) = \pm 2[/tex]
Step-by-step explanation:
If the given expression is,
[tex](x + 2)^2 - 9 = -5[/tex]
For solving this expression, By adding 9 on both sides,
[tex](x+2)^2 = 4 [/tex]
By taking square root on both sides,
[tex]\sqrt{(x+2)^2} = \sqrt{4}[/tex]
[tex]({(x+2)^2)^{\frac{1}{2} = \pm 2[/tex] [tex]( \text{ Because, }\sqrt{4} = \pm 2 \text { and }\sqrt{x} = x^{\frac{1}{2}})[/tex]
[tex]{(x+2)^{2\times \frac{1}{2} = \pm2[/tex] [tex]((a^m)^n=a^{m\times n})[/tex]
[tex](x + 2) = \pm2[/tex]
Which is the required next step.
help which statement is true
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Saturn mass = 6 x 10^26 = 6,000 x 10^23
6000/3 = 2000
so answer is bottom right
Saturn has about 2,000 times more mass
The altitude of a triangle is increasing at a rate of 1 cm/ min while the area of the triangle is increasing at a rate of 2 cm2 / min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm2 ?
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The rate of change of the base of a triangle, given an increase of the altitude at 1 cm/min and an increase in area at 2 cm2/min, when the altitude is 10 cm and the area is 100 cm2, is 4 cm/min.
Explanation:The subject of this question is related to the field of calculus, specifically dealing with determining the rate of change, or the derivative, of a function. We're asked to determine the rate at which the base of the triangle is changing when the altitude is 10 cm and the area is 100 cm2, given that the altitude of the triangle is increasing at a rate of 1 cm/ min and the area of the triangle is increasing at a rate of 2 cm2 / min.
We know that the area of a triangle is given by the formula 1/2 * base * height. When it comes to rates, we can differentiate this with respect to time t to get dA/dt = 1/2 * (base * dh/dt + height * db/dt) where dA/dt is the rate of change of the area, dh/dt is the rate of change of the height, and db/dt is the rate of change of the base.
Given that dA/dt = 2 cm2/min and dh/dt = 1 cm/min, and we are finding db/dt when the height is 10 cm and the area is 100 cm2, we substitute these values to solve for db/dt. This simplifies to find that the base is increasing at a rate of 4 cm/min.
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Find the maximum and minimum values of f(x,y) = 8x+y for the polygonal convex set having vertices at (0, 0), (4, 0), (3, 5), (0, 5).
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This means, f is a function where we plug in pairs of numbers.
then, f calculates the first number times 8, to which it then adds the second number we plugged.
let's calculate f for the vertices:
f(0,0)=8*0+0=0+0=0
f(4, 0)=8*4+0=32+0=32
f(3, 5)=8*3+5=24+5=29
f(0, 5)=8*0+5=0+5=5
the maximum value of f is 32
the minimum value of f is 0
If f(x) = 3/x+2 - √x-3, complete the following statement (round to the nearest hundredth) f(7)= PLEASE HELP ME
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f(7)=3/9-sqrt(4)
f(7)=1/3-2 = 1/3-6/3 = -5/3 = -1.67
The value of given function f(7) is -1.8.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
According to the given problem,
f(x) = [tex]\frac{3}{x + 5}- \sqrt{x - 3}[/tex]
At x = 7,
⇒ f(7) = [tex]\frac{3}{7 + 5} - \sqrt{7-3}[/tex]
⇒ f(7) = [tex]\frac{1}{4} - 2[/tex]
⇒ f(7) = [tex]-\frac{7}{4}[/tex]
⇒ f(7) = - 1.75
≈ -1.8
Hence, we can conclude, the value of function f(7) is -1.8.
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How can you use models find the volume of composite figures
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if log75=1.875
then what is the value of log (sub 100) 75?
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so ... log(sub100) X = logX /2!
and log(sub100)75 = 1.875/2 = 0.9375
Answer: The required value of [tex]\log_{100}75[/tex] is 0.9375.
Step-by-step Explanation: Given that [tex]\log 75=1.875.[/tex]
We are to find the value of the following logarithm :
[tex]log_{100}75.[/tex]
We will be using the following properties of logarithm :
[tex](i)~\log_ba=\dfrac{\log a}{\log b}\\\\\\(ii)~\log a^b=b\log a.[/tex]
Therefore, we have
[tex]\log_{100}75\\\\\\=\dfrac{\log 75}{\log100}\\\\\\=\dfrac{1.875}{\log10^2}\\\\\\=\dfrac{1.875}{2\times\log10}\\\\\\=\dfrac{1.875}{2}~~~~~~~~~~~[since~\log10=1]\\\\\\=0.9375.[/tex]
Thus, the required value of [tex]\log_{100}75[/tex] is 0.9375.
You pick cards one at a time without replacement from an ordinary deck of 52 playing cards. what is the minimum number of cards you must pick in order to guarantee that you geta)two pair (for example, two kings or two 5s)b)three of a kind (for example, three 7s)
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To guarantee two pairs, a player must pick at least 14 cards from a deck of 52 playing cards without replacement. For three of a kind, a minimum of 16 cards is required. This is an example of sampling without replacement, where each selection affects subsequent draws.
Explanation:To determine the minimum number of cards one must pick from a standard deck of 52 playing cards to guarantee getting two pairs, consider the worst-case scenario where you pick one card of each rank before getting any pair. Since there are 13 different ranks, picking 13 single cards wouldn't guarantee a pair, but the 14th card will definitely match one of the previously drawn ranks, thus forming a pair. To ensure two pairs, you could go through another 13 cards without getting a match to your first pair, so the 15th card would be the second pair. Therefore, you must pick at least 14 cards to guarantee two pairs.
For three of a kind, you pick sequentially from the different ranks. After picking one card of each of the 13 ranks, the 14th card will form a pair, and the 15th card could potentially be of a new rank. However, the 16th card drawn must either create a pair with another rank or a 'three of a kind' with the rank that already has two. Thus, the minimum number of cards one must pick to guarantee a three of a kind is 16.
In sampling without replacement, drawn cards are not returned to the deck, making each draw dependent on the previous ones. This contrasts with sampling with replacement, where each draw is independent since cards are returned to the deck and reshuffled after each pick.
Find the sum of a finite geometric sequence from n = 1 to n = 8, using the expression −2(3)^n − 1.
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an=-2(3)^(n-1)
will be:
when:
n=1
an=-2
when n=2
a2=-6
when n=3
a3=-18
when n=4
a4=-54
when n=5
a5=-162
when n=6
a6=-486
when n=7
a7=-1458
when n=8
a8=-4374
thus the summation of the term will be:
Sn=(-4374+-1458+-486+-162+-54+-18+-6+-2)
Sn=-6560
the answer is -6560
what is the midpoint of 45-53
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the midpoint of (4, 5) ; (5, 3) is : ((4+5)2 , ((5+3)/2)
(9/2 , 4)
Find the ratio of the increase in price to the original price.
$6.60 to $11.00 per case of 12 quarts
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Christine is putting money into a savings account. She starts with $550 in the savings account, and each week she adds $60 . Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Christine has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 19 weeks.
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Let's write the equation.
550 + 60w = s
Now put in our value for w.
550 + 60 · 19 = 1690
The answers are
550 + 60w = s
And
1690
Hope this helps! :)
You have to multiply the amount of money she gets each week by the number of weeks to get the total amount saved. You also have to incorporate the starting amount of $550 so you have to add that to whatever Christine has saved.
To find the amount in her savings account after 19 weeks you just have to substitute 19 for w and solve it.
60*19+550=s
Multiply first
1140+550=s
and your answer is:
$1,690=s
Leah likes to stretch 5 minutes for every 10 minutes of dancing. How many minutes should she stretch if she is doing a 50 minute dance class?
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5/10=?/50
We know that ten times 5 equals 50, so we can multiply the numerator, 5, by 5 to get our answer (what you do to the denominator, you must also do to the numerator).
5x5=25
The answer is 25,
Leah should stretch for 25 minutes during a 50-minute dance class, as she stretches for 5 minutes for every 10 minutes of dancing.
Leah stretches for 5 minutes for every 10 minutes of dancing. To calculate how much time she should be stretching during a 50-minute dance class, we need to apply a simple ratio. For every 10 minutes of dance, she stretches for 5 minutes, which is half the time spent dancing. We can set up the proportion as follows: 5 minutes of stretching / 10 minutes of dancing = X minutes of stretching / 50 minutes of dancing.
Now, solving for X gives us 5/10 = X/50, which simplifies to X = (5/10) × 50 = 25 minutes. Therefore, Leah should stretch for 25 minutes during her 50-minute dance class.
Find the volume of a right circular cone that has a radius of 4 inches and a height of 12 inches
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Final answer:
The volume of a right circular cone with a radius of 4 inches and a height of 12 inches is calculated using the formula V = (1/3)πr²h, resulting in a volume of 64π cubic inches.
Explanation:
The question asks to find the volume of a right circular cone with a specific radius and height. To calculate the volume of a cone, you use the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone. Since we're given the radius as 4 inches and the height as 12 inches, we substitute these values into the formula: V = (1/3)π(4²)(12).
Carrying out the calculation, we have V = (1/3)π(16)(12) = (1/3)π(192) = 64π inches³. Therefore, the volume of the cone is 64π cubic inches.