Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.

Answer: 30.

Step-by-step explanation:

[tex]7\frac{1}{2} =\frac{7*2+1}{2} \\\frac{14+1}{2}=\frac{15}{2}\\ \frac{15*2}{2*2}=\frac{30}{4} \\ \frac{30}{4}=30*\frac{1}{4} .[/tex]

There are total 30 quarters in [tex]7\frac{1}{2}[/tex].

A quarter is one out of four equal parts. One quarter is the same as the fraction ¼.

A fraction represented with its quotient and remainder is a mixed fraction.

To change a mixed fraction to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.

According to the given question.

We have a mixed fraction [tex]7\frac{1}{2}[/tex].

So, the improper fraction of the given mixed fraction is given by

[tex]7 \frac{1}{2} = \frac{15}{2}[/tex]

To find the number of quarters in the given mixed fraction, we will divide [tex]7\frac{1}{2}[/tex]  by  [tex]\frac{1}{4}[/tex].

Therefore,

[tex]\frac{7\frac{1}{2} }{\frac{1}{4} }[/tex]

= [tex]\frac{\frac{15}{2} }{\frac{1}{4} }[/tex]

[tex]= \frac{15\times 4}{2}[/tex]

[tex]= 15\times 2[/tex]

[tex]= 30[/tex]

Hence, there are total 30 quarters in [tex]7\frac{1}{2}[/tex].

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Answer: -8 points

Step-by-step explanation: because he lost 50, and he originally had 42, a smaller number, the answer will go into the negatives.

42-50= -8, which is how you get the answer!

Answer:

-8

Step-by-step explanation:

42-50 is the same as 50-42, except the answer is negative

Answer:

25 minutes

Step-by-step explanation:

If it takes 5 minutes to prepare one game we need to multiply 5 games by 5 minutes: 5*5 = 25 minutes

Answer:

probability of all the four women chosen over people needed in a committee=4 over 4 =1

The cost spent on fill the box with sand is 405$.

According to the statement

we have given a square sandbox with length 9 ft and depth of 1 ft.

and the rupees of sand per cubic ft is $5

then

Now, we have to find the volume of sandbox with the given length and depth.

So, for this purpose we use Volume formula

V = (a)^3

V = 9*9*1

V = 81 cubic feet

And the cost of sand per cubic feet is $5.

then

The cost of sand for 81 cubic per feet is calculate by multiplication formula then

Total cost of sand = 81*5

Total cost of sand = 405$

So, The cost spent on fill the box with sand is 405$.

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The polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.

In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.

To find the solutions, we do as follows:

x³ - 4x² - 7x + 28 = 0,

or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},

or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},

or, (x - 4)(x² - 7) = 0 {Grouping},

or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex]}.

By the zero-product rule, the solutions are:

x - 4 = 0, or, x = 4,

x + √7 = 0, or, x = -√7,

x - √7 = 0, or, x = √7.

Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.

Thus, the polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.

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The complete question is:

"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?

x³-4x²-7x+28=0

a. two or zero

b. three or one

c. one

d. two"

Answer:

Two or zero.

Step-by-step explanation:

Answer:

$0.45.

Step-by-step explanation:

Total amount of money held by all 5 children

= 5 * 0.50 = $2.50.

After 0.25 is lost the total = $2.25.

So the new average = 2.25 / 5

= $0.45.

Answer:

605

Step-by-step explanation:

We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.

110 + 1/2(1100 - 110)  Subtract what is in the parentheses

110 + 1/2(990) Find 1/2 of 990

110 + 495

604

Answer:

a. x² + 10x + 25

Step-by-step explanation:

because

(x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25

so, it is a perfect square of (x + 5).

The mean distance is increased by a factor of [tex]2^{3/2}[/tex] if the orbital period  of planet y is twice that of the planet x.

Description of the Kepler's law.

The orbital period T and the mean distance from the sun, A, expressed in astronomical units (AU), are related in accordance with Kepler's third law.

The mathematical formula is,

T² = A³

Here, T denotes the orbital period and A represents the average separation or mean distance from the sun.

Now, if T(y) = 2T(x)

⇒ A'³(y) = 2A³(x)

A'(y) = [tex]2^{3/2}[/tex]A(y)

Thus, if orbital period of planet y is twice the orbital period of planet x, the mean distance is lengthened by a factor of [tex]2^{3/2}[/tex].

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Answer:

2 Superscript three-halves

Step-by-step explanation:

Edge

Answer:

9,240

Step-by-step explanation:

For the first number, there are 22 numbers available to choose from. For the second number, there are 21 numbers available, since the first number cannot be the same as the second number. And for the last number, there are 20 remaining numbers to choose from. So, there are 22*21*20=9240 possible sequences.

Ms. Drake will earn [tex]\$ 170[/tex] in this time from the investment of [tex]\$ 1000[/tex] at a simple interest with rate of interest [tex]8.5\%[/tex]

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Formula for finding simple interest is [tex]\frac{principal \times rate \ of \ interest \times time}{100}[/tex]

Given principal of Ms. Drake is [tex]\$1000[/tex]

Rate of interest is [tex]8.5 \%[/tex]

Time is [tex]2[/tex] years.

Interest [tex]=\frac{1000 \times 8.5 \times 2}{100}[/tex]

            [tex]=\frac{17000}{100}\\=170[/tex]

Therefore, Ms. Drake will earn [tex]\$ 170[/tex] in this time.

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A 99% confidence interval for the population mean of high school students that take the bus to school every day is b) ci=(44.34%, 54.43%)

We need to find the 99% confidence interval for the population mean of high school students that take the bus to school everyday

A confidence interval is a range of estimates for an unknown parameter. The confidence interval is calculated at the specified confidence level; the most common is the 95% confidence level, but sometimes other levels are used, such as 90% or 99%.

The confidence interval of proportions is given by:

π ± z √(π (1-π) /n)

π is the sample proportion.

z is the critical value.

n is the sample size.

For 99% confidence interval the value of z is 2.58

π = 321/650

The confidence interval is given by

=321/650 ± 2.58 √( (321/650) × [ 1 - (321/650) ] ÷ 650)

= (0.493846 ± 0.050594)

=(0.4434 , 0.5443)

=(44.34 % , 54.43 %)

Hence a 99% confidence interval for the population mean of high school students that take the bus to school every day is ci=(44.34%, 54.43%)

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Answer:

the scale factor is :

[tex]\frac{9}{15}[/tex]

Step-by-step explanation:

The trapezoids TUVW and ABCD are similar

and AB is the corresponding side of the side TU

Then the function that transform TUVW to ABCD is of scale factor :

[tex]= \frac{AB}{TU}[/tex]

[tex]= \frac{9}{15}[/tex]

Check the picture below, so the parabola looks more or less like that one, with a "p" distance of 2 units that is positive, whilst the vertex, which is always half-way between the focus point and the directrix is where you see it there, thus

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-1\\ k=2\\ p=2 \end{cases}\implies 4(2)( ~~ x-(-1) ~~ )~~ = ~~(y-2)^2\implies 8(x+1)=(y-2)^2 \\\\\\ x+1=\cfrac{1}{8}(y-2)^2\implies \boxed{x=\cfrac{1}{8}(y-2)^2-1}[/tex]

Answer: UR WELCOME

Step-by-step explanation: ANSWER ON EDMENTUM

Intermediaries who are independent, but agree to cooperate have likely formed a(n) contractual distribution system.

The most commonplace form of Contractual VMS is Franchising. In franchising, the manufacturer authorizes the distributor to promote its product below the producer's call against some annual license rate. For example, McDonald's, Dominos, Pizza Hut, etc. are all styles of a franchise that might be operating on a contractual foundation.

A form of vertical advertising machine in which unbiased firms at unique degrees of distribution are tied together by using contracts to achieve economies of scale and more income impact.

A vertical advertising system refers to a marketing system that aims to draw and attain organizations running inside the same industry. then again, horizontal advertising and marketing device refers to an advertising and marketing system whereby corporations which can be on equal degree join collectively to advantage economies of scale.

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Answer:

[tex]AC = \bf 4.13 \space\ cm[/tex]

Step-by-step explanation:

Using Pythagoras's theorem:

[tex]\boxed {a^2 = b^2 + c^2}[/tex],

where:

a ⇒ hypotenuse (AC, ? cm)

b, c ⇒ the two other sides of the triangle (AB = 2.2 cm, BC = 3.5 cm),

we can find the length of AC.

[tex]AC^2 = AB^2 + BC^2[/tex]

⇒ [tex]AC^2 = (2.2)^2 + (3.5)^2[/tex]

⇒ [tex]AC = \sqrt{(2.2)^2 + ((3.5)^2}[/tex]

⇒ [tex]AC = \sqrt{17.9}[/tex]

⇒ [tex]AC = \bf 4.13 \space\ cm[/tex]

The correct answer is FV = $11,323.38  

What is compound interest explain?

FV = PV x [1 + R]^N, where FV=Future Value, PV=Present Value, R=Interest rate per period, N=Number of periods.

FV = 9,000 x [1 + 0.047]^5

FV = 9,000 x 1.047^5

FV = 9,000 x 1.258152857750007

FV = $11,323.38

Therefore , the answer is $11,323.38.

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The length of side DF is 3.75.

Given that within the figure there are two triangles that are similar.

Congruent triangles will be triangles that have a comparable measure and shape. This infers that the comparing sides are comparable and the relating focuses are equivalent.

Two comparative triangles are given.

If two triangles are comparable at that point their comparing sides are relative and comparing points are congruent.

DF/AB=EF/BC

Substitute the values from the given figure

DF/15=6/24

Cross multiply both sides, and we get

DF×24=6×15

DF×24=90

Divide both sides by 24, we get

(DF×24)/24=90/24

DF=15/4

DF=3.75

Hence, the length of side DF from the given figure is 3.75.

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The parent function of g(x) = |x - 7| +6 is f(x) = |x|

The function is given as:

g(x) = |x - 7| +6

The above function is an absolute function, and the parent function is f(x) = |x|

Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|

When f(x) is reflected across the x-axis, we have:

f'(x) = -|x|

When f(x) is reflected across the y-axis, we have:

f'(x) = |x|

When f(x) is stretched horizontally by a factor k

g'(x) = |kx|

When f(x) is stretched vertically by a factor k

g'(x) = k|x|

When f(x) is shifted horizontally by k units

f'(x) = |x ± k|

When f(x) is shifted vertical by k units

f'(x) = |x| ± k

See attachment for the graph of g(x)

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Answer:

Step-by-step explanation:

Let the length be l and the width be y. We have the following:

l + w = 37

lw = 342

From here, we can find the factor pairs of 342, and see which pair has a sum of 37. Our desired pair is 18 & 19, so the dimensions of the field are 18 by 19 feet.

Answer:

[tex]y = -x^{2} +4x-10[/tex]

Step-by-step explanation:

I used a graphing calculator to calculate the points so I'm not sure how to do it without, but I hope this helped!

Answer:

Step-by-step explanation:

If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have

Answer:

Step-by-step explanation:

Area = h/2 (b_1+b_2)

[tex]\sf\cfrac{7}{2}\:(22+34)[/tex]

Add 22 and 34 = 56

[tex]\sf \cfrac{7}{2} \times 56[/tex]

Let's express 7/2 * 56 as a single fraction:-

[tex]\sf \cfrac{7\times 56}{2}[/tex]

Multiply 7 and 56 = 392

[tex]\sf \cfrac{392}{2}[/tex]

Divide

[tex]\sf 196[/tex]

Therefore, the area of the trapezoid is 196cm².

_______________________

Answer:

12

Step-by-step explanation:

The area of a triangle is calculated with the following formula:

[tex]\frac{1}{2} *b*h[/tex] (b: base, h: height (or legs))

We can use this formula to find the length of the other leg:

30 = [tex]\frac{1}{2} *b*h[/tex] multiply both sides with 2 to get rid of fraction

60 = b*h one of the leg's length is given as 5 so

60 = 5*h divide both sides by 5

12 = h is the length of the missing leg.

Answer:

1

Step-by-step explanation:

[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]

Answer:

946

Step-by-step explanation:

Let's make an equation :

34% of x = 321.8

Covert 34% into decimal by dividing by 100 :

34 ÷ 100 = 0.34

Rewrite equation with decimal form :

0.34x = 321.8

Divide both sides by x to make x the subject :

x = 321.8 ÷0.34

x = 946.470588235

To the nearest whole number will be 946 as 4 rounds it down

So our final answer will be 946

Hope this helped and have a good day

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{34}{100} \sdot x = 321.8[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{(321.8) \sdot(100)}{34} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 946.47[/tex]

Round off to nearest whole number :

[tex]\qquad \sf  \dashrightarrow \: x = 946[/tex]

The answers are as follows:

a. There are 6 ways of tossing a coin and then drawing a marble from the bag. (Tree diagram is shown in the diagram below) The probability is 1/12.

b. These are independent events since tossing a coin does not affect the drawing of marble from the bag.

c. From the tree diagram, the probability of tossing a head and drawing a red marble is 1/6(since they are independent events).

d. The probability of drawing two blue marbles if the first marble is not replaced is 1/5(since they are dependent events).

It is given that a bag contains,

Number of white marbles(W) = 1

Number of Blue marbles (B) = 3

Number of Red marbles (R) = 2

Thus, there are 6 marbles in the bag. So, the sample space for drawing a marble = 6

a. Finding all the possible outcomes using a tree diagram:

The possible outcomes from the tree diagram are

(H, W), (H, B), (H, R), (T, W), (T, B),  and (T, R)

The probability of tossing head or tail = 1/2

The probability of drawing a marble from the bag = 1/6

So, the compound probability = (1/2)(1/6) = (1/12)

The sample space for this is 12.

b. Independent or dependent events:

These are independent events since the tossing of a coin does not affect the drawing of marble from the bag.

c. Finding the probability of tossing a head and drawing a red marble:

The probability of tossing a head = 1/2

The probability of drawing a red marble = 2/6 = 1/2

Since they are independent events,

The required probability = (1/2)(1/2) = 1/4

d. Finding the probability of drawing two blue marbles if the first marble is not replaced:

The probability of drawing a blue marble from the bag(1st attempt) = 3/6

The probability of drawing another blue marble from the bag (2nd attempt) = 2/5 (From the leftover marbles after the first attempt)

Since they are dependent events, the probability of the 2nd event is calculated only after the first event is calculated.

So, the required probability = (3/6)(2/5) = 1/5

Thus, all the probabilities are calculated.

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Area covered with grass seed = 10.4[tex]m^{2}[/tex].

What is trapezoid geometry?

A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.

Area of the trapezoid ={ (a+b)/2} +h

where a and b is base and h is height of the trapezoid geometry.

In the question,

a=6m , b=7m and h=4m.

According to the formula { (a+b)/2} +h.

Area covered with grass seed = {(6+7)/2} + 4

                                                    = 10.4[tex]m^{2}[/tex].

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Answer:

26

Step-by-step explanation:

GOT IT RIGHT`

Hello,

an other method

Pythagorean theorem :

x² + x² = 6²

2x² = 36

x² = 36/2

x² = 18

x = √18 (and not -√18 because x ≥ 0)

x = √(9 × 2)

x = √(3² × 2)

x = 3√2

Answer A