Answer:
a) The volume of the dunking booth = 98 feet³
b) They will need 84 feet³ of water to fill 6/7 of dunking booth
Step-by-step explanation:
* Lets talk about the rectangular prism
- It has 6 rectangular faces each two opposite faces are congruent
- It has three dimensions Length, Width and Height
- Its volume = Length × Width × height
* In our problem the dunking booth is a rectangular prism
with dimensions:
- Width = 3.5 ft
- Length = 3.5 ft
- Height = 8 ft
∴ Its volume = 3.5 × 3.5 × 8 = 98 feet³
a) The volume of the dunking booth = 98 feet³
* They want to fill 6/7 of the dunking booth with water
∴ The volume of the water will be 6/7 from the volume
of the dunking booth
∵ The volume of the dunking booth = 98 feet³
∴ The volume of the water = 6/7 × 98 = 84 feet³
b) * They will need 84 feet³ of water
a) 98
b) 84
hope this helps!
the diagram shows three different bicycle routes taken by Frank,alexis,and juan to get to the electronics store. Frank-8kilo Alexis-6kilo juan ? kilometers
Answer:
10 km
Step-by-step explanation:
8^2+6^2=10^2
Answer:
Juan traveled 10 km.
Step-by-step explanation:
is also right on EDGEN.
A teacher has 24 students in her class. She wants to divide them into 4 equal groups. Write an expression to represent the number of students in each group.
let's set up an equation
4x=24
solve normally:
x=6
so the expression is 4x=24 and she can have 6 kids in each group
A circle has an area of 153.86 units2 and a circumference of 43.96 units. If the radius is 7 units, what can be said about the relationship between the area and the circumference? (Use 3.14 for .) A. The ratio of the area to the circumference is equal to half the radius. B. The ratio of the area to the circumference is equal to twice the radius. C. The ratio of the area to the circumference is equal to the square root of the radius. D. The ratio of the area to the circumference is equal to the radius squared.
Answer:
Option A. The ratio of the area to the circumference is equal to half the radius
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
The ratio of the area to the circumference is equal to
[tex]\frac{A}{C}=\frac{\pi r^{2}}{2\pi r}[/tex]
Simplify
[tex]\frac{A}{C}=\frac{r}{2}[/tex]
Verify
In this problem
[tex]A=153.86\ units^{2}[/tex]
[tex]C=43.96\ units[/tex]
[tex]\frac{A}{C}=\frac{153.86}{43.96}=3.5\ units[/tex]
and [tex]3.5\ units[/tex] is equal to half the radius
therefore
The ratio of the area to the circumference is equal to half the radius
Answer:
A: The ratio of area of circle to the circumference is equal to half the radius.
Step-by-step explanation:
We are given that area of a circle=153.86 square units
Circumference of circle=43.96 units
Radius of circle=7 units
We have to find that the relation ship between area of circle and circumference of circle
Area of circle=[tex]\pi r^2[/tex]
Circumference of circle=[tex]2\pi r[/tex]
Ratio of area of circle to the circumference=[tex]\frac{\pi r^2}{2\pi r}[/tex]
Ratio of area of the circle to the circumference of the circumference=[tex]\frac{1}{2} r[/tex]
Ratio of area to the circumference=[tex]\frac{153.86}{43.96}=\frac{7}{2}=\frac{r}{2}[/tex]
Hence, option A is true.
Answer:A: The ratio of area of circle to the circumference is equal to half the radius.
What is the inverse of the function
f
(
x
)
=
−
1
2
(
x
+
3
)
f(x)=−
2
1
Answer:
f
−
1
(
x
)
=
2
x
+
6
?
f^-1(x)=2x+6 is the answer i believe
Answer:
−2x−3
Step-by-step explanation:
I don't know if right
Which best describes the graphs of the line that passes through (0,2) and (6,4) and the line that passes through (2,1) and (5,7)?
Answer:
The line which has slope 1/3 is a shallow line.
The line which has slope 2 is a steep line.
Both are increasing.
Step-by-step explanation:
Compare the lines by finding the slope between each pair of points.
Using the slope formula, substitute the points.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-2}{6-0} = \frac{2}{6} = \frac{1}{3}[/tex]
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{5-2} = \frac{6}{3} = 2[/tex]
The line which has slope 1/3 is a shallow line.
The line which has slope 2 is a steep line.
Amir has a stand where he sells lemonade for $1.00 per cup and packages of chocolate chip cookies for $1.50. If he earns $280 on his first weekend and sells twice as many cups of lemonade as packages of cookies, how many of each did he sell? Wrote and solve a system of equations.
Answer:
160 cups of lemonade and 80 packages of cookies.
Step-by-step explanation:
l = lemonade
c = cookies
l+1.5c=280
2c=l
Substitute.
3.5c=280
Simplify.
c=80
Substitute into the second equation.
l=160.
Plug it back into the equations to check.
What expression is equivalent to 4(2x+1)-(-6x)
The expression 4(2x+1)-(-6x) simplifies to the equivalent expression 14x + 4 using the distributive property and the rule for subtracting negative numbers.
Explanation:The expression given is 4(2x+1)-(-6x). To simplify this expression, we should use the distributive property and also the rule that subtracting a negative is the same as adding a positive.
Let's break down the steps:
First, distribute the 4 inside the parentheses: 4 × 2x + 4 × 1, which gives us 8x + 4.Next, consider the term -(-6x). Subtracting a negative number is equivalent to adding: -(-6x) = +6x.Finally, combine the like terms: 8x + 6x + 4 which simplifies to 14x + 4.The equivalent expression for the given problem is found to be 14x + 4.
company A charges $50 to come to the house plus $60 per hour company B charges $80 to come to the house plus $50 per hour how many hours will it be for bills to be the same
Answer:
3 hours
Step-by-step explanation:
You own 6 pairs of jeans and want to take 2 of them with you on vacation,in how many ways can you choose 2 pairs of jeans?
A-10
B-12
C-15
D-20
Answer:
your answer is 20. Hope this helped! :)
Step-by-step explanation:
Answer:
Step-by-step explanation:
its 15
Describe a square using geometric vocabulary
Answer:
parallelogram with equal diagonals that bisect the angles
Step-by-step explanation:
A square is a geometric shape with four equal sides and four right angles. Its diagonals are equal and bisect each other at right angles. The perimeter is calculated as 4 times the side length, and the area is the side length squared.
A square is a fundamental geometric shape, characterized by several distinct properties:
A square has four equal sides, meaning each side has the same length.It has four right angles, with each angle measuring 90 degrees.The diagonals of a square are equal in length and bisect each other at right angles, dividing the square into four right-angled isosceles triangles.The perimeter of a square can be calculated as 4 times the length of one side (P = 4s).The area of a square can be calculated as the side length squared (A = s²).For example, if each side of a square is 2 feet long,
area= 2 feet x 2 feet = 4 square feet.
These geometric properties make squares an important figure in mathematics and are often found in various structures and designs, emphasizing clarity and symmetry.
52,940 written in expanded form
Answer:
Fifty two thousand nine hundred forty
Step-by-step explanation:
Thank you!!
Please mark this as the brainliest one!!!
A father who is 42 years old has a son and a daughter. The daughter is three times as old as the son. In at present? 10 years, the sum of all their ages will be 100 years. How old are the two siblings
Answer:
The son is 7 and the daughter is 21
Step-by-step explanation:
So, if they’re his kids they must be younger than him which means that both ages are more than 42. One number also has to be the other one times 3. 7*3 = 21 and they are also both less than 42. That means it’s your answer.
Brainliest please
After 10 years, the two siblings are 12 years and 36 years old.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
A father who is 42 years old has a son and a daughter.
The daughter is three times as old as the son.
Let x be the age of the son, then 3x be the age of the daughter.
After 10 years, the sum of all their ages will be 100 years.
That means,
x + 10 + 3x + 10 + 42 = 100
4x = 48
x = 12
Then 3x = 36.
Therefore, the ages of the siblings are 12 and 36.
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Analyze the diagram below and complete the instruction that follow.
Answer:
x=10
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
7x-3 + 12x-7 = 180
Combine like terms
19x-10 = 180
Add 10 to each side
19x-10+10 = 180+10
19x = 190
Divide by 19
19x/19 = 190/19
x= 10
Answer:
10
Step-by-step explanation:
We are given a diagram which we are to analyze and and solve for x.
We can see the a straight line is intersected by another line thus forming two angles which are supplementary. It means that the sum of these angles is equal to 180 degree.
So we can write them as:
[tex] ( 7 x - 3 ) + ( 12 x - 7 ) = 180 \\\\ 12 x + 7 x = 180 + 3 + 7 \\\\ 19 x = 190 \\\\ x = \frac { 190 } { 19 }\\\\ x = 10 [/tex]
Therefore, the correct answer option is 10.
A group of students were asked whether they take French class, Art class, both classes or neither classes. The table shows the probabilities of the results
Art | Not Art | Total
French | 0.2 | 0.4 | 0.6
Not French | 0.35| 0.05 | 0.4
Total | 0.55 | 0.45 | 1.00
Let A represent taking French class and B represent taking Art class.
Which statement is true?
A. Taking Art class and taking French class are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .
B. Taking Art class and taking French class are independent events because P(A|B)=P(A) and P(B|A)=P(B) .
C. Taking Art class and taking French class are independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .
D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .<<<<<<<
Answer: D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .
Step-by-step explanation:
We know that for dependent events A and B , the conditional probability of getting a given that B is given by :-
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
From the given table, if A represent taking French class and B represent taking Art class.
Then P(A)=0.6
and P(B)=0.55
[tex]P(\cap B)=0.2[/tex]
Now, [tex]P(A|B)=\dfrac{0.2}{0.55}=0.036363\approx0.036[/tex]
[tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.2}{0.6}=0.33333\aprox0.333[/tex]
Clearly, [tex]P(A|B)\neq P(A)[/tex]
[tex]P(B|A)\neq P(B)[/tex]
Therefore taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .[ By definition of independent events]
The correct statement is D; Taking Art class and taking French class are not independent events.
Consider A represent taking a French class and B represents taking an Art class.
The formula to determine whether two events are independent or not is P(A and B) = P(A) x P(B),
where P(A and B) is the probability of both events happening together, P(A) is the probability of event A happening, and P(B) is the probability of event B happening.
D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B).
This statement is incorrect because the formula to determine whether two events are independent or not is;
P(A and B) = P(A) x P(B),
not P(A|B) ≠ P(A) and P(B|A) ≠ P(B).
Using the values in the table:
P(A) = 0.6 (taking French class)
P(B) = 0.55 (taking Art class)
P(A and B) = 0.2 (taking both classes)
P(A and B) ≠ P(A) x P(B)
0.2 ≠ 0.6 x 0.55
The correct statement is option D.
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Please help it will help so much
Answer:
8:10
Step-by-step explanation:
If you add the amount of minutes it takes for her to get ready, then add them to 7:15 (55 minutes after 7:15) you get 8:10
The answer is d. I already did the math on the calculator
A football field is 100 yards long and 60 yards wide. Whats the length of a diagonal of the football field
Answer:
pythag. theorem
100^2 +60^2 =c^2
10,000+3600= (take sq. root) 13,600
c= 116.62ft
Step-by-step explanation:
The length of the diagonal of the football field is 116.62 yards.
What is the Pythagorean theorem?The Pythagorean theorem states that in a right-angled triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse.
The length of the diagonal can be found as follows:A football field is rectangular in shape.
The diagonal of a rectangle divides it into two right-angled triangles.
Therefore, the diagonal becomes the hypotenuse of the right-angled triangles.
Therefore, diagonal² = length² + width²
⇒ diagonal² = 10,000 + 3600 yards²
⇒ diagonal² = 13,600 yards²
⇒ diagonal = 116.62 yards
Therefore, the length of the diagonal of the football field is 116.62 yards.
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The recipe for Jack's Famous Chili uses 222 teaspoons (\text{t})(t)left parenthesis, t, right parenthesis of red hot chili powder for each cup (\text{c})(c)left parenthesis, c, right parenthesis of tomato sauce.
His rival, Marsha, claims her chili is spicier. She makes chili in large quantities, and uses the chart below.
Whose chili is spicier?
Chili powder (\text{t})(t)left parenthesis, t, right parenthesis Tomato sauce (\text{c})(c)left parenthesis, c, right parenthesis
444 3.53.53, point, 5
888 7.07.07, point, 0
121212 10.510.510, point, 5
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Jack's
(Choice B)
B
Marsha's
(Choice C)
C
They are equally spicy.
The spiciness of chili is determined by comparing the proportion of chili powder to tomato sauce. Jack consistently uses 222 teaspoons of chili powder per cup of sauce, whereas Marsha's ratio varies, but never exceeds 126.86 teaspoons per cup. Therefore, Jack's chili is spicier.
Explanation:To determine whose chili is spicier, we must compare the ratio of chili powder to tomato sauce used by Jack and Marsha. Jack uses 222 teaspoons of chili powder for every 1 cup of tomato sauce. For Marsha, we'll have to establish the ratios based on her table.
When Marsha uses 444 teaspoons of chili powder, she uses 3.5 cups of tomato sauce. So, her ratio for this batch is 444/3.5 = 126.86 teaspoons of chili powder per cup of sauce.When Marsha uses 888 teaspoons her ratio is 888/7 = 126.86 teaspoons per cup.When she uses 1212 teaspoons, her ratio is 1212/10.5 = 115.43 teaspoons per cup.Regardless of the quantity she makes, Marsha's ratio never goes below 115.43, which is less than Jack's ratio of 222. So, Jack's chili is spicier than Marsha's.
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HELP ME!!!!!
Mike pays $0.02 in sales tax for every $1 that he
spends. If Mike buys $60 worth of items, what is
the total cost?
A $60.00
B $0.02
C $1.20
D $61.20
Answer:
1.20
Step-by-step explanation:
you multiply 0.02 by 60 usually 120 but 2 decimal points so move the decimal 2 to the left
solve for x 6=1 over 3x+5
[tex]6 = 1 \: \over 3x + 5[/tex]
HELP PLZZZZ BRAINLIEST! Which stem-and-leaf plot represents the data 10, 70, 37, 65, 88, 86, 70, 10, 15, 15, 15?
Answer:
The correct answer is C.
Step-by-step explanation:
For stem leaf plot, the only thing you do is put the number on the tens place under "stem" and the number on the ones place under "leaf".
The stem-and-leaf plot that represents the data is the Stem and leaf of option C.
Option C is the correct answer.
What are stem and leaf?In statistics, a stem-and-leaf plot is a way to display a set of numerical data in a visual format that allows for easy analysis of the distribution of the data.
We have,
The data are:
10, 70, 37, 65, 88, 86, 70, 10, 15, 15, 15
This can be written in stem and leaf form as:
Stem and leaf of option C.
Now,
There are 5 numbers where the first value is 1.
i.e
10, 10, 15, 15, and 15.
This can be seen in the Stem and leaf of option C.
Thus,
The stem-and-leaf plot that represents the data is the Stem and leaf of option C.
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What is the inverse function of f(x)= 4- x/6
Answer:
[tex]f^{-1}(x) = 6(4-x) = 24-6x[/tex]
Step-by-step explanation:
Let [tex]y=f(x)[/tex] and swap x and y:
[tex]x = 4 - \frac{y}{6}[/tex]
Then, rearranging for y:
[tex]x+\frac{y}{6} = 4[/tex]
[tex]\frac{y}{6}= 4-x[/tex]
[tex]y= 6(4-x) = 24-6x[/tex]
Final answer:
Explaining the inverse function of a given function.
Explanation:
Inverse function of f(x) = 4 - x/6:
Replace f(x) with y: y = 4 - x/6.
Swap x and y: x = 4 - y/6.
Solve for y: y = 24 - 6x.
Which description can be written as the expression 8/21n?
A the quotient of twenty-one times a number and eight
B the product of eight and twenty-one times a number
C the quotient of eight and twenty-one times a number
D the product of twenty-one times a number and eight
Answer with explanation:
We have to describe the rational number in words
[tex]=\frac{8}{21 n}[/tex]
Dividend =8
Divisor =21 n
Quotient
[tex]=\frac{\text{Dividend}}{\text{Divisor}}\\\\=\frac{\text{Eight}}{\text{Twenty one} \times \text{A number}}[/tex]
Option C: → The quotient of eight and twenty-one times a number
Solve −3.5 = x 4 for x using the multiplication property of equality.
Answer:
x = -14
Step-by-step explanation:
-3.5 = x/4
In the right side, the fraction x/4 means x divided by 4. We want x alone, so we multiply both sides by 4.
-3.5 * 4 = x/4 * 4
-14 = x
Answer: x = -14
The solution to the equation -3.5 = x/4for x using the multiplication property of equality is x = -14.
What is multiplication property of equality?Multiplication property of equality is an equality property which states that if both the sides of an equation are multiplied by the same number, the expressions on the both sides of the equation are equal.
So,
-3.5 = x/4
multiply both sides by 4
-3.5 × 4 = x/4 × 4
-14 = x
Therefore, x equals negative 14.
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A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream the speed of the boat in Stillwater is 15 mph greater than the speed of the current find the speed of the current
Final answer:
To find the speed of the current, we can set up equations for the boat's downstream and upstream speeds and solve for the current speed.
Explanation:
To find the speed of the current, let's assume the speed of the boat in still water is x mph. Since the boat's speed downstream is 60 mph, we can set up the equation:
(x + c) * t = 60
Where 'c' represents the speed of the current, and 't' represents the time taken. Similarly, the equation for the upstream speed of the boat (36 mph) can be written as:
(x - c) * t = 36
Simplifying these equations, we get:
x + c = 60/t
x - c = 36/t
Adding these equations, we obtain:
2x = 96/t
Solving for x, we get:
x = 48/t
Substituting this value back into one of the original equations, we can solve for t:
(48/t) + c = 60/t
Simplifying, we find:
c = 12/t
Therefore, the speed of the current is inversely proportional to the time taken for the downstream and upstream journeys.
so if marissa walks from her home to the store, then to the park,then back home. How far does she walk in all?
Answer:
1 23/24
Step-by-step explanation:
Add up distance between park, home, and store. 7/8 + 1/4 + 5/6 = 47/24
Turn into mixed number (simplest form). 1 23/24 miles
Which statements is an axiom of euclidean geometry?
A. If two lines intersect, their intersection is a plane.
B. If two planes instersect, their intersection is a point.
C. If two points lie in a plane, the line containing those points lies in the same plane.
D. If two points lie in a plane, the line containing those points lies in the same plane.
E. Given any two points A and B, there are exactly two lines that contain those points.
Answer:
C. If two points lie in a plane, the line containing those points lies in the same plane.
D. If two points lie in a plane, the line containing those points lies in the same plane.
Best regards
What is 8 7/8 in simplest form
Answer:
it's already in simplest form, as a decimal it would be 8.875
Step-by-step explanation:
The problem involves adding mixed numbers. First, convert them to improper fractions, add them up, and convert back to mixed numbers if possible. The first equation results in [tex]5\frac{1}{2}[/tex] while the second results in [tex]8\frac{7}{8}[/tex].
Explanation:The student is asking this question in the context of addition of fractions. To tackle these problems, the first thing to do is to switch both numbers into improper fractions.
In equation 1,
[tex]4\frac{1}{6} +1\frac{2}{6} \\= \frac{25}{6} + \frac{8}{6} \\=\frac{33}{6} \\=\frac{11}{2} \\=5\frac{1}{2}[/tex]
In equation 2,
[tex]7\frac{4}{8} + 1\frac{3}{8}\\ =\frac{60}{8} + \frac{11}{8}\\ =\frac{71}{8}\\ =8\frac{7}{8}[/tex]
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Can you guys pls help me out
Answer:
A. $240,000
Step-by-step explanation:
look at the chart - find $30,000 and find 35 year old / 75%.. go down and to the right of the chart and find 8.0.. multiply 30,000 by 8.0 = 240,000.
hope this helps!!
Point A is located at (-3, -6) and is reflected in the y-axis. What is the location of Point A'?
(3, -6)
(-3, 6)
(-6, -3)
(3, 6)
Answer:
(3, -6)
Step-by-step explanation:
The formula for reflecting across the Y axis is that the X axis value will become opposite, so the -3 becomes positive 3.
Answer:
(3, -6)
Step-by-step explanation:
When you reflect a point (x, y) in the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,
(-3, -6)⟶ (3, -6)
The image below shows the point before and after the reflection.
F(x)=x^2-3x-2 is shifted 4 units left. The results is g(x). What is g(x)?
Answer:
B. [tex]g(x)=(x+4)^2-3(x+4)-2[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=x^2-3x-2[/tex]
If [tex]f(x)[/tex] is shifted to the left 4 units and the result is [tex]g(x)[/tex].
Then;
[tex]g(x)=f(x+4)[/tex]
We substitute [tex](x+4)[/tex] into [tex]f(x)=x^2-3x-2[/tex] to find the [tex]g(x)[/tex].
[tex]g(x)=(x+4)^2-3(x+4)-2[/tex]
The correct choice is B.