Clark made a model of his house. his house was 30 1/2 feet long. The dimensions of the model were 1/25 the dimension of Clark's actual home. what is the length, in feet, of the model.

Using the the Distributive Property to express 64 + 24 is 88.

This property states that multiplying the sum of two or more addends by a number produces the same result as multiplying each addend separately by the number and then adding the products together.

When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar terms, we usually add the numbers first and then multiply by 5. 5(10 + 3) = 5(13) = 65.

In this case, 64 + 24 will be;

= 8(8 + 3)

= 88

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The answer to the given function -1 . f(-8) -4 . g(4) is -7.

What are functions?

The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.

According to question, we see that f(-8)=-5, and g(4)=3

Now substituting in the given equation:

-1 . f(-8) -4 . g(4)

=(-1 . -5) - (4 . 3)

=5-12 = -7

Therefore the answer to -1 . f(-8) -4 . g(4) is -7

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The rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station is 313.05 mi/h .

Given :

a plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station .

Here ,

h = 2

d = 3

we know that ,

x = [tex]\sqrt{d^2 - h^2}[/tex]

= [tex]\sqrt{3^2 - 2^2}[/tex]

= [tex]\sqrt{9 -4}[/tex]

= [tex]\sqrt{5}[/tex]

d = [tex]\sqrt{5}[/tex] * 420 / 3

= [tex]\sqrt{5}[/tex] * 140

= 313.05 mi/h

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Answer:

[tex]60=4x\\\\15=x[/tex]

I hope this helped.

Answer: y = -4x+60

y is -4 times x plus 60

a) The percentile of the phone that sold for $330 is; 29%

b) The sales price at 75th percentile is; $425

In statistics, a percentile is a term that describes how a score compares to other scores from the same set.

From the given set of data showing the sales prices, let us sort them out from smallest to largest;

Sort the data values from smallest to largest:

235, 299, 300, 304, 325, 325, 330, 345, 355, 355, 370, 400, 400, 405, 415, 415, 425, 430, 449, 450, 495

It should be noted that 6 of the 21 data values are smaller than 325.

The percentile is then the number of data values that are less than the individual's data value divided by the number of data values in total, written as a percentage.

Thus;

Percentile = (Total number of data values/Number of data values that are less than the individual’s data value) × 100%

= 6/21  × 100%

≈ 0.2857 × 100%

= 28.57 % ≈ 29%

At 75th percentile, we have;

0.75 = x/21

x = 21 * 0.75

x = 15.75

Thus, the selling price of the phone at the 75th percentile is greater than 16 of the 21 phones. This phone has a selling price of at least $425

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There are 210 sequences for 7 church bells to rung with the given conditions. Using permutations, the required number of sequences is calculated.

A sequence or arrangement that can be framed by taking some or all of a finite set of things (or objects) is called a permutation.

The formula for finding the number of such arrangements is,

ⁿPₓ = n!/(n - x)!

It is given that, a church's bell tower has 7 bells. 3 of them will ring in a sequence before each service and no bell is rung more than once.

So, the number of sequences that the bells will form is calculated by using the permutations formula. I.e., ⁿPₓ = n!/(n - x)!

Here, n = 7; x = 3

Then,

ⁿPₓ = n!/(n - x)! ⇒ ⁷P₃ = 7!/(7 - 3)! = 7!/4!

⇒ ⁷P₃ = (7 × 6 × 5 × 4!)/4! = 7 × 6 × 5 = 210

Therefore, there are 210 sequences for ringing the bells.

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Answer:

(2, -7)

Step-by-step explanation:

4x + y = 1                   3y= 6x + 27

y = 1 - 4x

3(1 - 4x) = 6x + 27

3 - 12x = 6x + 27

-12x = 6x + 24

-18x = 24

6/3

2

y = 1 - 4x

y = 1 - 4(2)

y = 1 - 8

y = -7

4x + y = 1

Answer:

Step-by-step explanation:

4x + y = 1
Divide 4x by 4, then do the same to the 1

4x/4 + y = 1/4

= x + y = 0.25

If you are solving for x, then the equation will look like this.

x = 0.25 - y (minus because you are moving the variable to the other side of the = sign)

If you are solving for y, then the equation will look like this.

y = 0.25 - x (minus because you are moving the variable on the other side of the = sign)

Answer solving for x = x = 0.25 - y

Answer solving for y = y = 0.25 - x

-------------------------------------------------------------------------------------------------------------

3y = -6x + 27

3y/3 = -6x + 27/3

y = -6x + 9

Bring -6x to the other side of the =.

6x + x = 9

6x/6 + y = 9/6

x + y =  1.5

Then you have to move the variable depending on which one you are going to solve for.

Answer solving for x = 1.5 - y

Answer solving for y = 1.5 - x

Hope this helps!

Answer:q<-6.87

Step-by-step explanation:

isolate q by adding 2.01 to both sides

-q>6.87

divide by side by -1, and since it is negative flip the sign

q<-6.87

Answer:

142.10 units²

Step-by-step explanation:

[tex] A = \dfrac{n}{360^\circ}\pi r^2 [/tex]

[tex] A = \dfrac{134^\circ}{360^\circ}\pi \times 6^2 [/tex]

[tex] A = \dfrac{134^\circ}{360^\circ}\pi \times 6^2 [/tex]

[tex] A = 142.10~units^2 [/tex]

Answer: 56

Step-by-step explanation: 23+5=56

Option A) Buying a laptop will be most affordable among all the options as per the Selling price with Sales tax included.

The selling price is the price at which a thing is sold. Typically, it is identified as SP. also known as a selling price on occasion.

Shop owners essentially mark this as a promotional item to give discounts to customers in a way that,

When a product is sold to a buyer, the government levies sales tax (abbreviated as ST). This tax will be collected by the merchant and paid to the government. As a result, it is added to the bill after being charged on the item's selling price.

For Laptop,

Selling Price = (100-40)% of 2399.99

                     = 60% of 2399.99 = $ 1439.99

Total bill = 1439.99 + 8.2% of 1439.99

              = 1439.99 + 118.08 = $ 1558.07

For Smart TV,

Selling Price = (100-10)% of 1799.99

                     = 90% 0f 1799.99 = $ 1619.99

Total bill = 1619.99 + 4.5% of 1619.99

               = 1619.99 + 72.9 = $ 1692.89

For Iphone,

Selling Price = (100-5)% of 1699.99

                     = 95% 0f 1699.99 = $ 1614.99

Total bill = 1614.99 + 6.8% of 1614.99

               = 1614.99 + 109.82 = $ 1724.81

For GeForce RTX 3090 Graphics Card,

Selling Price = 2199.99 - 500 = $ 1699.99

Total bill = 1699.99 + 7.5% of 1699.99

               = 1699.99 + 127.5 = $ 1827.49

Total bill

Graphics Card > Iphone > Smart TV> Laptop.

Option A) Buying a laptop will be most affordable among all the options.

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The solution to the system of equations is (d) (-2, 1)

From the question, we have the following parameters that can be used in our computation:

y = 2x + 5

y = -1/4x + 0.5

Substitute y = 2x + 5  in the equation y = -1/4x + 0.5

So, we have the following representation

-1/4x + 0.5 = 2x + 5

Collect the like terms

So, the equation becomes

2x + 1/4x = 0.5- 5

So, we have

2.25x = -4.5

Divide by 2.25

x = -2

Substitute x = -2 in y = 2x + 5

y = 2 x -2 + 5

y = 1

Hence, the solution is (d) (-2, 1)

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Using the Pythagorean theorem, we know that the roof of the building is 24 ft far from the ground.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, the Pythagorean theorem formula:

c² = a² + b²

Now, substitute the values in the formula to calculate the distance between the roofline and the ground.

c² = a² + b²

25² = a² + 7²

625 = a² + 49

a² = 625 - 49

a² = 576

a = √576

a = 24ft

Therefore, using the Pythagorean theorem, we know that the roof of the building is 24 ft far from the ground.

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Answer:

Function • Quadratic Function •

Absolute Value Inequalities • Linear Function

[tex]\cfrac{2}{3}-\cfrac{5}{12}\implies \cfrac{(4)2~~ - ~~(1)5}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{8~~ - ~~5}{12}\implies \cfrac{3}{12}\implies \cfrac{3\cdot 1}{3\cdot 4}\implies \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4}{5}+\cfrac{11}{12}\implies \cfrac{(12)4~~ + ~~(5)11}{\underset{\textit{using this LCD}}{60}}\implies \cfrac{48~~ + ~~55}{60}\implies \cfrac{103}{60}\implies 1\frac{43}{60}[/tex]

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.

Let us take the radius of the circle to be r

We know that circumference = 2πr and the area of a circle is πr²

As, Scale factor = Original circle / Scaled circle

From the question, scale factor = 2

Thus,

2 = Circumference of the Original circle / Circumference of the Scaled circle.

⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle

For the area as well, scale factor = 2

2 = Area of the Original circle / Area of the Scaled circle

⇒ Area of the scaled circle = (1/2) * Area of the original circle

Thus,

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

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The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.

Let us take the radius of the circle to be r

We know that circumference = 2πr and the area of a circle is πr²

As, Scale factor = Original circle / Scaled circle

From the question, scale factor = 2

Thus,

2 = Circumference of the Original circle / Circumference of the Scaled circle.

⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle

For the area as well, scale factor = 2

2 = Area of the Original circle / Area of the Scaled circle

⇒ Area of the scaled circle = (1/2) * Area of the original circle

Thus,

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

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Since 3 | 1+3 | = 3 |4|

                      = 3·4

                      = 12

and

since 3 | -7+3 | = 3 |-4|

                        = 3·4

                        = 12,

both 1 and -7 check as solutions,

so C: x = 1 or x = -7

A small airplane can fly about 124.8 miles in one hour.

In this question, we have been given a small airplane flew 104 miles in 50 minutes.

We need to find the distance the airplane would cover in an hour.

Let a small airplane can fly 'x' miles in one hour.

We know that 1 hour = 60 minutes

Using proportionality we get an equation,

x/104 = 60/50

We solve above equation.

50x = 60 * 104

x = 6240/50

x = 124.8

So, the distance would be 124.8 miles

Therefore, an airplane can fly 124.8 miles in an hour.

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As per the congruence theorem, we have proved that ΔABC ≅ΔDEF.

In math congruence theorem states that if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.

Here we need to prove ΔABC ≅ΔDEF by using the congruence theorem.

Here we have given that ΔABC and ΔDEF,

=> ∠B≅∠E [right angle]

So, we have obtained that

=> ∠A≅∠D

As we know that there is two angles and one non included side of ΔABC is congruent the two corresponding angles and one non- included side of ΔDEF, therefore, by AAS congruence rule.

So, based on the given fact we have identified that

=> ΔABC ≅ΔDEF

Therefore, the AAS congruence postulate defined that the triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

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Answer:

7x - y = 5

Step-by-step explanation:

(y - y1) = m(x - x1)

Here, (x1, y1) = (1, 2) and m = 7

(y - 2) = 7(x - 1)

y - 2 = 7x - 7

7x - y - 7 = - 2

7x - y = -2 + 7

7x - y = 5

Answer:The standard form of the equation of the line through the given point with the given slope through:(1, 2), slope = 7 is 7x - y = 5.

Step-by-step explanation:

f(x) and g(x) are not inverses because f(g(x)) and g(f(x)) do not both equal x.

For a function f:X—>Y, its inverse f^{-1}:Y—>X  admits an explicit description,

it sends each element y∈Y to the special element x∈X

such that, f(x)=y.

Hence, f(x) and g(x) are not inverses because f(g(x)) and g(f(x)) do not both equal x.

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Answer: 150+30n ≤ p

Step-by-step explanation:

150 is your starting amount, and you add 30 lbs of how many ever boxes (n) onto your plane. So far, you have 150 + 30n. Because there is a limit of p amount that you can't exceed, you need a less than or equal to sign because it can be p amount but not over p amount. So your answer is 150 +30n ≤ p

We can conclude there is an association between age group of the viewer and amount of violence watched and its  55+ year-olds are likely to be categorized as low-violence.

What is segmented bar graph?

In a stacked (or segmented) bar graph:

The horizontal axis still represents one variable, with every bar representing one in every of the catgories of the variable.

Each bar is segmented in step with the classes of the second variable. or else, every bar will be seen as being created from smaller bars stacked on high of every different.

Main body:

We can know from the graph The older the age, the more the Tow-violence, 55+ year-olds are likely to be categorized as low-violence"

so there is an association Choose D

Hence ,  we can conclude there is an association between age group of the viewer and amount of violence watched and its  55+ year-olds are likely to be categorized as low-violence.

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Students will board the bus at 1350 even though it is not totally full.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few cmmon units for measuring area

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

723+685

1408-58

1350

Hence, Students will board the bus at 1350 even though it is not totally full.

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Answer:

----------------------------------------

The perimeter is:

If the perimeter is less than 20, then the inequality is:

Answer:

x < 4

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Therefore, from inspection of the triangle:

⇒ Perimeter = 4 + 9 + x + 3

⇒ Perimeter = x + 16

If the perimeter is less than 20 meters then:

⇒ x + 16 < 20

Solve the inequality:

⇒ x + 16 - 16 < 20 - 16

⇒ x < 4

Answer:

[tex]122.5[/tex]

Step-by-step explanation:

[tex]circumference \: = 2\pi \:r[/tex]

[tex]\pi = 3.14[/tex]

[tex]r = 19.5[/tex]

Replacing:

[tex]2 \times 3.14 \times 19.5 = 122.46[/tex]

Therefore, final answer[tex] = 122.5[/tex](to the nearest tenth)

The answer is 122.5

In the given question, we have given the radius of the circle and we need to find the circumference of the same.

To need to find the circumference, we must recall this formula

Circumference of circle = [tex]2\pi r[/tex]

Now, according to the question

Radius = 19.5 cm

Circumference = 2 * [tex]\pi[/tex] * 19.5

                         = 2 * 3.14 * 19.5       (Taking [tex]\pi[/tex] = 3.14)

                         = 122.5 cm

Therefore, the circumference of a circle with radius 19.5 cm is 122.5 cm

On rounding off the answer to the nearest tenth, it remains the same.

Hence, the final answer to the question is 122.5 cm.

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For the function, y = log₄ (x + 16) - 1, it has x-intercept of -12 and y-intercept of 1.

Logarithmic functions are functions expressed in another way for exponential functions. It is the power to which any number should be raised to yield other values.

Logₐ x = n can be written in exponential form as x = aⁿ.

y = log₄ (x + 16) - 1

x-intercept is the x-coordinate of the point when y = 0.

0 = log₄ (x + 16) - 1

For the left hand side to be equal to 0, the term log₄ (x + 16) must be equal to 1.

log₄ (x + 16) = 1  

⇒ x + 16 = 4       (∵ logₐ a = 1)

⇒ x = -12

y-intercept is the y-coordinate of the point where x = 0.

y = log₄ (0 + 16) - 1

y =  log₄ (16) - 1

y =  log₄ (4²) - 1

logₐ mⁿ = n logₐ m

⇒ y = 2 log₄ (4) - 1

⇒ y = 2 - 1     (∵ log₄ (4) = 1)

⇒ y = 1

Hence, the function y = log₄ (x + 16) - 1 has x-intercept of -12 and y-intercept of 1.

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To test the null hypothesis that there is no difference in parents' wealth for the different levels of schooling, a one-way ANOVA (analysis of variance) test should be used.

To compare the means of two or more groups, statisticians employ the analysis of variance (ANOVA) test. It is used to assess whether there are any significant variations in the means of the groups and to pinpoint which group or groups have significantly different means. The null hypothesis, according to which there is no difference between the group means, is evaluated using the ANOVA test using the F-statistic. If the F-statistic is significant, at least one of the groups has a mean that differs from the others in a meaningful way. To examine how several treatments or circumstances affect a response variable, investigations frequently utilize an ANOVA. It can also be used in non-experimental research to compare the means of different groups.

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