Answer: I believe the answer to this question is: X= 1/5.
A factory makes sheets of metal that are 2/3 of an inch thick. If a worker at the factory makes a stack of 8 of the sheets, how many inches thick will the stack be?
Write your answer as a fraction or as a whole or mixed number.
The thickness of a stack of 8 sheets of metal, each 2/3 of an inch thick, is 5 1/3 inches.
To determine the thickness of a stack of 8 sheets of metal that are each 2/3 of an inch thick, we simply multiply the thickness of one sheet by the number of sheets in the stack:
(2/3 inch/sheet) x 8 sheets = (2/3) x 8
Now, we simplify the expression by multiplying 2 by 8 which equals 16, and then we keep the same denominator:
16/3 inches
This fraction can also be converted to a mixed number:
5 1/3 inches
So, the stack will be 5 1/3 inches thick.
A home owner is building a square patio and will cover the patio with square tiles. Each tile has an area of 256 square inches and costs $3.45 each. The home owner has \$500 to spend on tiles. Calculate how many tiles the home owner can buy. Find the side length
(in feet) of the largest patio the home owner can build.
Answer:
The homeowner can buy 144 tiles maximum.
Side length = 16 feet.
Step-by-step explanation:
The cost of each tile is $3.45.
So, at $500, the homeowner can buy [tex]\frac{500}{3.45} = 144.92[/tex] ≈ 144 number of tiles. {As the number of tiles can not be a fraction.}
Since each tile is a square with area 256 square inches, so the homeowner can arrange the tiles in 12 by 12 arrangements.
Each tile has side length = √256 = 16 inches.
So, the side length of the largest patio is (16 × 12) inches = 16 feet. (Since, 1 foot = 12 inches). (Answer)
Show how to use unit multipliers to convert 4 hours to seconds.
Answer:
4 hours = 14400 seconds.
Step-by-step explanation:
i) In 1 hour there are 60 minutes
ii) in 1 minute there are 60 seconds
iii) therefore 1 hour = 60 minutes
= 60 [tex]\times[/tex] 60 seconds
= 3600 seconds
iv) therefore to convert 4 hours to seconds we have to multiply the number of hours by 3600 seconds
therefore 4 hours = 4 [tex]\times[/tex] 3600 seconds = 14400 seconds.
A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8° when staring at the top of the statue. Then the person looks down at an angle of 14° when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?
Answer:
The statue is 22.24 ft tall.Step-by-step explanation:
The given question says that, the man is standing 50 ft away from the statue.
Looking at the top of the statue, the angle of elevation is 8°.
Hence, where the man is standing, from that horizontal plane, the distance of the top of the statue is [tex]50 tan 8°[/tex].
Similarly, looking down towards the base, the angle is 14°.
Hence, the height from the base of the statue to the horizontal plane, where the man is standing is [tex]50 tan 14°[/tex].
The total height of the statue is [tex]50 tan 8° + 50 tan 14° = 50( tan 8° + tan 14°)[/tex] = 22.24475804 ≅22.24 ft.
This graph shows how the length of Karen's essay depends on the number of hours she spends writing this week.
What is the constant of variation?
Type your answer as a decimal.
pages per hour.
Answer: [tex]0.8[/tex] pages per hour.
Step-by-step explanation:
For this exercise it is important to know that, by definition, Direct variation equations have the following form:
[tex]y=kx[/tex]
Where "k" is the constant of variation.
Therefore, it is a straight line that passes through the origin.
In this case, given the graph attached in the exercise, you can follow these steps in order to find the constant of variation:
Step 1: You need to choose any point on the line. Let's choose the point (5,4).
Step 2: Now you must ubstitute the coordinates of that point into [tex]y=kx[/tex]. Then:
[tex]4=k(5)[/tex]
Step 3: Finally, you must solve for the Constant of variation "k", in order to find its value. Therefore, you get that this is:
[tex]k=\frac{4}{5}\\\\k=0.8[/tex]
A dress that is regularly priced $80 is on sale for 30% off. What is the sale price of the dress?
Answer:
$56?
Step-by-step explanation:
I think you get 100%-30%=70%.
70%=0.70
0.70*$80= $56
Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A
enter the ratios in reduced form:
Answer:
see explanation
Step-by-step explanation:
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{20}{29}[/tex]
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{21}{29}[/tex]
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{20}{21}[/tex]
The functions sin, cos, and tan for a given angle in a right triangle are defined in terms of ratios of the side lengths. They are respectively the ratios of the opposite side to the hypotenuse, the adjacent side to the hypotenuse, and the opposite side to the adjacent side.
Explanation:In a right triangle, sin(A) is defined as the ratio of the side opposite to angle A (opposite side) to the hypotenuse, cos(A) as the ratio of the adjacent side to the hypotenuse, and tan(A) as the ratio of the opposite side to the adjacent side.
Suppose the lengths of the sides of the given right triangle are a, b, and c (where c is the length of the hypotenuse).
Then, sin(A) = a/c, cos(A) = b/c, and tan(A) = a/b. These ratios must be put in reduced form by simplifying the fractions if necessary.
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4 times the quotient of 3 and 4
Answer:
3
Step-by-step explanation:
You would start by dividing
3 by 4. Then multiply 3/4 and 4. The 4s would cancel out leaving you with 3. 3/ 4×4=3
hope this helps
Final answer:
To answer the student's question, first find the quotient of 3 and 4, which is ¾, and then multiply that result by 4 to get the final answer of 3.
Explanation:
The student is asking for the result of multiplying 4 with the quotient of 3 and 4. To solve this, first calculate the quotient of 3 and 4, which is ¾. Then, multiply this result by 4.
Step 1: Quotient of 3 and 4 = 3 ÷ 4 = ¾
Step 2: Multiply the quotient by 4 = ¾ × 4
When you calculate step 2, you get:
¾ × 4 = (3 × 4) / 4 = 3
So, 4 times the quotient of 3 and 4 is 3.
The physician tells a woman who usually drinks 5 cups of coffee daily to cut down on her coffee consumption by 75%. If this woman is compliant with the physician's instruction, how many ounces of coffee is she allowed daily?
Answer:
Step-by-step explanation:
5 cups per day.....1 cup = 8oz.....so 5 cups = (5 * 8) = 40 oz
cut down by 75%....means ur only drinking 25%
25% of 40 oz =
0.25(40) = 10 oz per day <===
In testing the effectiveness of an energy drink on the performance of athletes, 50 athletes were given water and 50 athletes
were given a new energy drink, Yellow Bull. After drinking, each athlete was asked to perform a one-mile run, a 100 yard sprint
and 20 pull-ups.
A) conclusion
B)hypothesis
C)dependent variable
D)independent variable
The correct answer is C; Dependent variable.
Further explanation:
Researchers are very interested in the dependent variable. This variable is what is being tested and measured during the research in progress. In this case, it is the new energy drink.
The researchers are looking for an effect to occur while changing the independent variable of the case study. There are three main different types of variables used in research studies, they are;
IndependentDependentControlWith the athletes doing exercises after consuming the test product, they are seeing if the product does give more energy than if they hadn't of consumed the energy drink.
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A mother is five times as old as her daughter. In 6 years, the mother will be three times as old as her daughter. How old is each now?
Answer: daughter = 6 years
mother = 30 years
Step-by-step explanation:
Let the daughter's age be x and the mother's age be y , then from the first statement
y = 5x .......................... equation 1
In 6 years time , the mother will be y + 6 and the daughter will be x + 6 ,from the second statement , we have
y + 6 = 3 ( x + 6 )
y + 6 = 3x + 18 ..................................... equation 2
substituting equation 1 into equation 2 , we have
5x + 6 = 3x + 18
5x - 3x = 18 - 6
2x = 12
x = 6
Therefore , the daughter's age is 6 years ,then the mother's age will be 6x5 = 30 years
What is (4x+5y)(2x+3y)
Answer:
8
x
2
+
22
x
y
+
15
y
2
Step-by-step explanation:
yeet
Answer:
Step-by-step explanation:
Are you cyclist travels at a rate of 1.8 km/min. how far will the cycle is travel in 48 minutes
Answer:
86.4 km
Step-by-step explanation:
Since the cyclist travels 1.8km in a minute, he will travel 48 times that in 48 minutes:
[tex]48*1.8 = 86.4[/tex]
Edin has £300 in his savings account.his bank offers him 5% simple intrest rate ped annum for a period of 3 years.how much intrest will he make after 3 years
Answer:
$45
Step-by-step explanation:
We are given the following information;
Money invested (Principal) is $300Rate of interest is 5% per annumTime the money is invested is 3 yearsWe need to determine the amount of interest the money will earn after three years.
Simple interest is calculated by the formula;Simple interest =(PRT) ÷ 100, Where P is the principal amount, R is the rate of interest and T is the time.Therefore, in this case;
Simple interest = ($300 × 5 × 3) ÷ 100
= $45
Thus, the money invested earned a simple interest of $45
Using the formula for simple interest, we find out that Edin will earn £45 as interest on his savings of £300 over a period of 3 years at a simple interest rate of 5% per annum.
Explanation:The subject of this question is simple interest. The formula for simple interest is: Principal * Rate * Time. Let's plug in the given values into the formula. Here, the principal amount is £300, the rate of interest is 5% per annum (or 0.05 in decimal form), and the time is 3 years. So, the calculation will be: £300 * 0.05 * 3.
After performing the calculation, we find that the interest Edin will earn after 3 years is £45.
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fill in the blanks 1 1/2 is ____ % of 7 1/2 ; 7 1/2 is ____ % of 1 1/2
Answer:
20; 500
Step-by-step explanation:
1.5 is what percent of 7.5. 7.5 is 5 times 1.5, so 1.5 is 1/5 of 7.5. 1/5=20%. Inversely, 7.5 is 5 times 1.5, 5=500%.
[tex]1 \frac{1}{2} \text{ is } \underline{20\%} \text{ of } 7 \frac{1}{2}[/tex]; [tex]7 \frac{1}{2} \text{ is } \underline{500\%} \text{ of } 1 \frac{1}{2}[/tex]
First, convert the mixed numbers to improper fractions:[tex]1 \frac{1}{2}[/tex] becomes [tex]\frac{3}{2}[/tex].
[tex]7 \frac{1}{2}[/tex] becomes [tex]\frac{15}{2}[/tex].
To determine the percentage, we use the percentage formula:[tex]\text{Percentage} = \frac{\text{part}}{\text{whiole}} \times 100\%[/tex]
Determine what percentage of [tex]1 \frac{1}{2}[/tex] is [tex]7 \frac{1}{2}[/tex]:[tex]\frac{\frac{3}{2}} {\frac{15}{2}} \times 100\% = \frac{3}{15}\times 100\% = \frac{1}{5}\times 100\% = 20\%.[/tex]
Thus,
[tex]1 \frac{1}{2} \text{ is } \underline{20\%} \text{ of } 7 \frac{1}{2}.[/tex]
For the second part, determine what percentage [tex]7\frac{1}{2}[/tex] is of [tex]1 \frac{1}{2}[/tex]:[tex]\frac{\frac{15}{2}} {\frac{3}{2}} \times 100\% = \frac{15}{3}\times 100\% = 5\times 100\% = 500\%.[/tex]
Thus,
[tex]7 \frac{1}{2} \text{ is } \underline{500\%} \text{ of } 1 \frac{1}{2}.[/tex]
Complete question:
fill in the blanks:
[tex]1 \frac{1}{2}[/tex] is ____ % of [tex]7 \frac{1}{2}.[/tex] ; [tex]7 \frac{1}{2}[/tex] is ____ % of [tex]1 \frac{1}{2}.[/tex]
A Line passes through the point (-1,-2) and is perpendicular to the line with the equation y= -x - 1 what’s the equation of the line
Answer:
y = x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x - 1 ← is in slope- intercept form
with slope m = - 1
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1, thus
y = x + c ← is the partial equation of the perpendicular line
To find c substitute (- 1, - 2) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = x - 1 ← equation of perpendicular line
- V17 is the geometric mean between 7 and what other number?
Answer:
[tex]\large\boxed{x=\dfrac{17}{7}}[/tex]
Step-by-step explanation:
[tex]\text{A geometric mean of}\ x\ \text{and}\ y:\\\\\sqrt{xy}\\\\\text{Let}\ x-\text{the number}.\\\\\text{Substitute:}\\\\\sqrt{17}=\sqrt{(7)(x)}\iff17=7x\qquad\text{divide both sides by 7}\\\\\dfrac{17}{7}=\dfrac{7x}{7}\to x=\dfrac{17}{7}[/tex]
How did i get the decimal in 16.2 by dividing by 48.6 and 3
Greatest to least 1/2 1/5 3/8
Answer:
1/5 3/8 1/2
Step-by-step explanation:
Why does it take 3 copies of 1/6 to show the amount as 1 copy of 1/2
3 copies of 1/6 makes it 1 copy 1/2 because 3 times of 1/6 is 3/6 which is 1/2
Step-by-step explanation:
3 times 1/6 = 3/6
which is 1/2.
Hence it takes 3 copies of 1/6 to show the amount as 1 copy of 1/2
Alternatively,
1/6+1/6+1/6= 1/2
3/6=1/2
1/2=1/2
how to simplify (2√5)²
(2√5 )²
= 2√5 × 2√5
= 4×5
= 20
A paper hat is folded into the shape of a kite, as shown.
A kite is shown. The left and right angles are right angles. The sides above the right angles are (3 x + 5) inches and (5 x + 1) inches. The sides below the right angle are (2 x + 1) inches and 5 inches.
What total length of ribbon is needed to line the two long sides of the hat?
Answer:
D is correct
Step-by-step explanation:
The total length of ribbon needed to line the two long sides of the hat is 22 inches.
Given that, the sides above the right angles are (3x + 5) inches and (5x + 1) inches. The sides below the right angle are (2x + 1) inches and 5 inches.
What are the properties of kites?A kite is a quadrilateral that has 2 pairs of equal adjacent sides. The angles where the adjacent pairs of sides meet are equal.
Now, (3x + 5)=(5x + 1)
⇒x=2
2x+1=5
⇒x=2
Thus, (3x + 5)=11 inches
Now, 11+11=22 inches
Therefore, the required answer is 22 inches.
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Alex wants to buy 4 pounds of peaches.They cost $1.20 per pound.How much will Alex need to spend for the peaches?
250 surveyed. 15 do not like pizza. 66% like pizza and burritos. 30% do not like burritos. Fill in the two way frequency table to show the results of the survey.
Answer:
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]
Step-by-step explanation:
250 people are surveyed. 15 of them do not like pizza, then
250 - 15 = 235 like pizza.
30% do not like burritos. 30% of 250 is
[tex]250\cdot 0.3=75[/tex] people which do not like burritos and 250 - 75 = 175 people like burritos.
Then the incomplete two way frequency table is
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&&&175\\\text{Do not like burritos}&&&75\\ \text{Total}&235&15&250\end{array}[/tex]
66% like pizza and burritos. Then
[tex]250\cdot 0.66=165[/tex] people like pizza and burritos.
Hence,
[tex]235-165=70[/tex] people like pizza and do not like burritos
[tex]175-165=10[/tex] people like burritos and do not like pizza
[tex]250-165-70-10=5[/tex] people do not like pizza and do not like burritos
Hence the complete two way frequency table is
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]
what is the answer of 1/4+1/5+1/6=
15/60+12/60+10/60= 37/60
What is the value of the expression below? (Four-fifths + three-fifths) + 3.5 times 5
Answer:
21
Step-by-step explanation:
Answer:
18 and 9/10
Step-by-step explanation:
if you add 4/5+3/5=7/5 or 1.4. 3.5*5=17.5, then you add them together to get 18.9 or in the fraction version= 18 and 9/10
Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.
A. The range for Week 1 equals the range for Week 2.
B. The range for Week 1 is greater than the range for Week 2.
C. The median for Week 1 is less than the median for Week 2.
D. The mean for Week 1 is greater than the mean for Week 2.
Answer:
The true statement is: A. The range for Week 1 equals the range for Week 2.
Step-by-step explanation:
Let's recall that the range of a data set is the difference between the largest number and the smallest number.
As we can confirm in the plot for week 1, the range is:
Range for week 1 = Largest number - smallest number
Range for week 1 = 89 - 62 = 27
In the same way, we can confirm in the plot for week 2 that the range is:
Range for week 2 = Largest number - smallest number
Range for week 2 = 89 - 62 = 27
Ranges for week 1 and 2 are equal, thus,
The true statement is: A. The range for Week 1 equals the range for Week 2.
For which values of A, B, and C will Ax + By = C be a vertical line through the point (8, 6)
Answer:
Step-by-step explanation:
a vertical line has an undefined slope....(8,6).....its equation is x = 8 because no matter what y is, x will always be 8.
but u need it in standard form Ax + By = C
so it is written as : x + 0y = 8 <===
A = 1
B = 0
C = 8
Ax + By = C will be a vertical line passing through point (8,6) for values of A = 1 , B = 0 and C = 8.
What is a vertical line ?
In a coordinate plane, a line parallel to the Y-axis is called vertical Line. Any point in this line will have the same value for the x-coordinate.
We know that the x-axis has lines that run vertical then if you have a point use your x-ordinate.
The equation of a vertical line is :
x = C
here : C is the value of the x- coordinates the line passes through.
In the given question we have to find out the values of A , B and C for which Ax + By = C be a vertical line passing through point (8,6).
Here , the coordinate of point (x , y) is (8 , 6).
So , the equation of vertical line will be x = 8.
So , if we compare it with the general form of line , Ax + By = C, then we get :
8A + By = 8
So , values of A , B and C :
A = 1, B = 0, C = 8
Therefore , Ax + By = C will be a vertical line through point (8,6) for values of A = 1 , B = 0 and C = 8.
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Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are normally $3.50 each, how many times must Seth attend in order for it to benefit his father to buy the pass?
Answer:
In order for it to benefit his father to buy the pass Seth have to attend the movies for 11 times.
Step-by-step explanation:
Given:
Cost of movie pass = $40
Cost per matinees with pass = $1.00
Cost per matinees without pass = $3.50
To Find:
Number of times must Seth attend in order for it to benefit his father to buy the pass = ?
Solution:
Let x be the number of times he wants to visit
To profit his father
The number of visits without pass = the number of visits with passin the cost of $3.50
Then, without pass if he visits for x times then the cost will be = 3.50x
Also with pass, the number of times he can visit the pass = [tex]\frac{40}{3.50}[/tex]
then
[tex]\frac{350 x}{3.50} = \frac{40}{3.50}[/tex]
[tex]3.50x = 40[/tex]
[tex]x = \frac{40}{3.50}[/tex]
x = 11.42
x = 11 (approx)
The area of the following rectangle is 24 square units.
Write an equation that can be used to find the value of n.
Solve the equation to find the value of n. In your answer, show all of your work.
Answer:
Step-by-step explanation:
Area of rectangle A = L × W
Length L = n - 3
Width = 2
Area = 24square unit
:- 24 = (n - 3)2
24 = 2n - 6 ...... This the equation
24 + 6 = 2n
30 = 2n
n = 30/2
n = 15