Eduardo has a recipe that uses 2/3 cup of flour for each batch .If he makes 4 batches ,how many cups of flour will he need? Write your answer as a mixed number. Use the number line to help.

Answer:

Length=96 feet

Width=70 feet

Step-by-step explanation:

Let the length = l

The width 26 feet less than its length=l-26

Perimeter of the giant rectangular movie screen= 332 feet

Perimeter of a rectangle = 2(L+W)

332=2(l+l-26)

332=2(2l-26)

Expanding the brackets

332=4l-52

4l=332+52

4l=384

l=384/4=96

The Length of the giant rectangular movie screen is 96 feet.

The Width, W=l-26=96-26=70 feet

The dimensions of the screen are: [tex]Length: 96\ feet[/tex] and [tex]Width: 70\ feet[/tex]

To find the dimensions of the IMAX screen, we need to set up a system of equations based on the given information. Let's denote the length of the screen by [tex]\( L \)[/tex] and the width by [tex]\( W \)[/tex].

Given:

1. The width is [tex]26 \ feet[/tex] less than the length: [tex]\( W = L - 26 \)[/tex]

2. The perimeter of the rectangle is [tex]332\ feet: \( 2L + 2W = 332 \)[/tex]

First, we can simplify the perimeter equation:

[tex]\[2L + 2W = 332\][/tex]

Divide both sides by [tex]2[/tex]

[tex]\[L + W = 166\][/tex]

Now, substitute the expression for [tex]\( W \)[/tex] from the first equation into the simplified perimeter equation:

[tex]\[L + (L - 26) = 166\][/tex]

Combine like terms:

[tex]\[2L - 26 = 166\][/tex]

Add 26 to both sides:

[tex]\[2L = 192\][/tex]

Divide both sides by [tex]2[/tex]

[tex]\[L = 96\][/tex]

Now that we have the length, we can find the width using the equation [tex]W = L - 26 \)[/tex]

[tex]\[W = 96 - 26 = 70\][/tex]

Answer:

Step-by-step explanation:

Answer:

3/35

Step-by-step explanation:

(15/50)×(14/49)

= 3/35 or 0.0857

Answer:

3/35.

Step-by-step explanation:

Probability (the first one selected has the decoder ring) = 15/50 = 3/10.

Probability (the second one selected has the decoder ring) = 14/49 = 2/7.

Therefore the probability that both have the ring =

3/10 * 2/7

= 6/70

= 3/35.

Note: The probabilities are multiplied because the 2 events are independent.

Answer:

The change in the value of Dave's shares = $ 105

Step-by-step explanation:

Total number of shares = 15

Let initial value of a share = x

On Monday, the value of each share rose = $ 2

Now the value of each share = x + 2

Total value of 15 shares on Monday = 15 (x + 2) -------- (1)

On Tuesday the value of each share fell = $ 5

Now the value of each share = x - 5

Total value of 15 shares on Tuesday = 15 (x - 5) --------- (2)

The change in the value of Dave's shares = 15 (x + 2) - 15 (x - 5)

⇒ 15 x + 30 - 15 x + 75 = 105

⇒ Thus the change in the value of Dave's shares = $ 105

Answer with Step-by-step explanation:

We are given that

LHS

[tex]\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)[/tex]

Using distribution property

[tex]a\cdot (b+c)=a\cdot b+a\cdot c[/tex]

[tex]\frac{1}{5}(5x)-\frac{1}{5}(20)-\frac{1}{2}(4x)+\frac{1}{2}(8)[/tex]

After multiplication we get

[tex]x-4-2x+4[/tex]

Combine like terms

[tex](x-2x)+(4-4)[/tex]

Then, we get

[tex]-x+0=-x[/tex]

Hence,verified.

Answer:D

Step-by-step explanation: I took the unit test

Answer:

A. small changes have been made within exact quotations.

Step-by-step explanation:

Brackets are pair of marks which enclose words or figures in order to separate them from the context. Thus, the use of brackets indicate that the quotation's exact punctuation has been adapted to the punctuation or grammar structure of the essay.

Answer:

65

62

Step-by-step explanation:

In inscribed quadrilaterals, opposite angles are supplementary.

First problem:

x + 148 = 180

x = 32

2x + 1 = 65

Second problem:

x + 20 + 3x = 180

x = 40

180 − (2x + 38) = 62

Answer:

25/6

Step-by-step explanation:

Because the line in the middle is an angle bisector, 5*10 = 12*x.

This means that 50 =12x, so 25/6 = x

Answer:

[tex]\sqrt[4]{7^5}[/tex]

Step-by-step explanation:

I apologize, I do not know how to explain this.

Answer:    

7⁵/₄

Step-by-step explanation:

⁴√7⁵

The fourth root is equivalent to the power 1/4.

= 7^(1/4 * 5)

= 7^(5/4).

Answer:

3 [tex]\frac{9}{20}[/tex]

Step-by-step explanation:

3.45=3 45/100

reduce and divided by 5

3 45/100= 3  9/20

Answer:

Step-by-step explanation:

add me on fortnite

The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.

To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.

Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:

P(20, 7) = 20! / (20 - 7)!

where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.

The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.

To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.

Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:

P(20, 7) = 20! / (20 - 7)!

where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.

Answer:

1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.

2. The intrusion of the younger rock by the principle of cross-cutting relationship

3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.

Step-by-step explanation:

In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.

The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.

The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.

The system has infinitely many solutions because both equations represent the same line in the coordinate plane. So C. Infinity many solutions will be the answer.

To determine the number of solutions for this system of equations, let's analyze it:

[tex]\[\left\{\begin{array}{l}x + y = 3 \\5x + 5y = 15\end{array}\right.\][/tex]

We can simplify the second equation by dividing both sides by 5:

[tex]\[x + y = 3\][/tex]

This equation is identical to the first equation in the system. So, the two equations represent the same line in the coordinate plane.

When two equations represent the same line, they have infinitely many solutions, because every point on the line satisfies both equations.

Therefore, the correct answer is:

(C) Infinitely many solutions

Complete Question:

Answer:24

Step-by-step explanation:

By setting up an equation c + 2c = 72, where 'c' represents cheese slices and '2c' represents pepperoni slices, and solving for 'c', we find there were 24 slices of pizza with just cheese.

To solve the problem about the number of pizza slices with different toppings, we can set up an equation based on the information given.

If 'c' represents the number of slices with just cheese, then 2c would represent the number of slices with pepperoni, because there are twice as many pepperoni slices as there are cheese slices. Since the total number of slices is 72, we can form the following equation:

c + 2c = 72

Combining like terms (c + 2c), we get 3c = 72. To find the value of 'c', we divide both sides of the equation by 3:

3c / 3 = 72 / 3

c = 24

Therefore, there were 24 slices of pizza with just cheese.

Answer: 60°

Step-by-step explanation:

When a figure has a rotational symmetry, it maps onto itself under rotation about a point at the centre.

When an hexagon rotate onto itself,

the vertices must cover to vertices and from sides to sides. There are six angles in a hexagon and the sum of the angles is 360°. Therefore, each angle has a measure of 360°/6 is equal to 60°.

Rotating subsequently by 60 degree will rotate a hexagon onto itself. A hexagon has 6 rotations, that is, a hexagon has a rotational symmetry of 6 and at angle 60°, the hexagon will rotate onto itself.

Answer:

a) Independent

b) Quantitative  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 517

Sample:

Married lawyers and their spouses.

Response variable:

Comparison of academic aptitudes of married lawyers and their spouses.

a) The given sampling is an example of independent sampling.

This is an independent sample because an individual of sample does not effect any other individual of the sample.

b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.

It is a quantitative measure because the scores can be expressed in numerical.

Answer:

The sampling is independent and the response variable is quantitative.

Explanation:

Given a random sample of [tex]517[/tex] couples

Learn more about Random sample, refer:

A system of equations can have no solution, one unique solution, or infinitely many solutions. A single solution indicates that the equations intersect at a point, no solution suggests parallel lines, and infinitely many solutions mean the equations are the same line expressed differently.

When discussing a system of equations, the possible solutions include having no solution, one unique solution, or infinitely many solutions. If a system has no solution, this typically means the equations represent parallel lines that never intersect. In contrast, if there is one solution, the equations represent two lines that intersect at a single point, such as the given solution (8, 2). The presence of infinitely many solutions indicates that the equations are the same line, represented in different forms, and thus they intersect at every point along the line.

To determine which of these scenarios applies to a particular system of equations, one should begin by determining the number of unknowns and the number of equations given. A single linear equation in two variables, such as those given in Practice Test 4 Solutions 12.1 Linear Equations, represents a line. A system composed of two linear equations can be solved using algebraic methods such as substitution or elimination.

If the system consists of the same equation expressed differently, such as y = 2x + 3 and 2y = 4x + 6, then they are essentially the same line, and the system would have infinitely many solutions.

Answer: her sales for the month of May is $55000

Step-by-step explanation:

Let x represent her total sales for the month of May.

Each month she receives a 5% commission on all her sales of medical supplies up to $20,000. This means that for her first sales worth $20000, she earns a commission of

5/100 × 20000 = 1000

She also earns 8.5% on her total sales over $20,000. This means that for sales over $20000, she earns

8.5/100(x - 20000) = 0.085x - 1700

Her total commission for May was $3,975. The expression becomes

1000 + 0.085x - 1700 = 3975

0.085x = 3975 + 1700 - 1000

0.085x = 4675

x = 4675/0.085

x = 55000

Kim's total sales for the month of May were $55,000. The first $1,000 of her commission came from the 5% commission on her first $20,000 in sales. The remaining $2,975 of her commission came from the 8.5% commission on her additional $35,000 in sales.

To find out Kim's sales for the month of May, let's first understand her commission structure. She earns a 5% commission on all her sales of medical supplies up to $20,000, and 8.5% on any of her total sales over $20,000. Her total commission for the month of May is given as $3,975.

If her sales were $20,000 or below, her commission would be 5% of that, which would be $1,000 at most. Her commision is definitely more than that, we can infer that her sales were more than $20,000.

To figure out her actual sales, we need to subtract $1,000 from her total commission of $3,975, which gives us $2,975. This amount is the commission she earned at the rate of 8.5% for sales over $20,000. To find out the sales corresponding to this commission, we should divide $2,975 by 8.5% (or 0.085). That gives us the sales amount over $20,000 as $35000.

Therefore, Kim's total sales for the month are the $20,000 she sold to make the first $1,000 of her commission, plus the additional $35,000. So Kim's total sales for the month of May were $55,000.

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The standard deviation is his IQ score above the mean is found by the Z score whose value is 4.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

It is given that,

Sample average, x = 160

mean, [tex]\mu[/tex] = 100

Standard deviation, [tex]\sigma =[/tex] 15

The Z-test value is found as,

[tex]\rm Z = \frac{x- \mu}{\sigma} \\\\ Z = \frac{160-100}{15} \\\\ Z = 4[/tex]

Thus, the standard deviation is his IQ score above the mean is found by the Z score whose value is 4.

Learn more about the standard deviation here:

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A student with an IQ score of 160 is 4 standard deviations above the mean IQ of 100 according to the given normal distribution, where one standard deviation equals 15 points.

To calculate how many standard deviations a score is above or below the mean, you can use the formula:

Z = (X - x) / SD

Where:

Applying this to the student's IQ score:

Z = (160 - 100) / 15

Z = 60 / 15

Z = 4

Therefore, a student with an IQ score of 160 is 4 standard deviations above the mean IQ, which is considered exceptionally high.

Answer:

The answer to your question is letter A

Step-by-step explanation:

Data

Factor                6n³  +  8n²  +  3 n +  4

- To factor this expression, factor the common terms of the first two factors

                        6n³ + 8n² = 2n²(3n + 4)

- Factor 1 in the second two terms    1(3n + 4)

- Factor all the expression by like terms      2n²(3n + 4) + 1(3n + 4)

                                                                     (3n + 4)(2n² + 1)

Answer:

I do not know sorry

Step-by-step explanation:

Answer:

x = 8, y = 4√3, z = 8√3

Step-by-step explanation:

Assuming that y is the altitude of the triangle (perpendicular to the hypotenuse), the triangles are similar.  So we can write proportions:

x / 4 = 16 / x

x² = 64

x = 8

4 / y = y / 12

y² = 48

y = 4√3

z / 12 = 16 / z

z² = 192

z = 8√3

Note: after finding one side, you can also use Pythagorean theorem to find the other two sides.

Answer:

a= 0.0897

b= 0.71186

Power of the test for detecting a true mean output voltage of 5.1 volts is 0.28814.

Step-by-step explanation:

See attached pictures.

The value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.

It is the ratio of favorable events to the total events.

Given

Standard deviation ([tex]\sigma[/tex]) = 0.25

[tex]\mu[/tex] = 5

n = 8

The acceptance region as

4.85 ≤ [tex]\rm \bar{x}[/tex] ≤5.15

a.  Then type I error of probability,

[tex]\alpha = P(4.85> \bar{x}\ when\ \mu =5) + P(\bar{x}\ > 5.15\ when\ \mu =5)\\\alpha = P(\dfrac{4.85-5}{0.25\sqrt{8} } > \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } ) + (\dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } > \dfrac{4.85-5}{0.25\sqrt{8} })\\\alpha = 2P ( z <-1.697)= 0.0897[/tex]

Where, [tex]z = \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} }[/tex]

b.  type II error

[tex]\beta = P(4.85 \leq \bar{x} \leq 5.15\ when\ \mu = 5.1)\\\beta = (\dfrac{4.85 - \mu}{0.25/\sqrt{8} }\leq \dfrac{\bar{x} - \mu}{0.25/\sqrt{8} }\leq \dfrac{5.15 - \mu}{0.25/\sqrt{8} }\ when\ \mu=5.1 )\\\beta = P(-2.8284\leq z\leq 0.5657)\\\beta = P(z\leq 0.5657)- P(z\leq -2.8284)\\[/tex]

therefore, the power of the test for detecting a true mean output voltage of 5.1 volt is

[tex]\begin{aligned} 1 - \beta &= 0.28281 \\\beta &= 0.71186\\\end{aligned}[/tex]

Thus, the value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.

More about the probability link is given below.

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Answer:

The smart-phone hit the ground when t = 7 s

Step-by-step explanation:

The height "h" is defined as:

h=16t^2 + 48t + 448

And, when the smart-phone hits the ground, h = 0 ft . Then,

16t^2 + 48t + 448 = 0

And this is a quadratic equation, and we can solve it using the formula for ax^2 + bx + c = 0, which is

x=[tex]\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]

So,

t = [tex]\frac{-48±\sqrt{48^{2} -4(-16)(448)} }{2(16)}[/tex]

t = [tex]\frac{-48±\sqrt{2304+28672} }{-32}[/tex]

And, we have two responses,

t_1 = [tex]\frac{-48+\sqrt{30976} }{-32}[/tex]    and    t_2 = [tex]\frac{-48-\sqrt{30976} }{-32}[/tex]

t_1 = - 4 s              and    t_2 = 7 s

As we know, the time is a quantity that cannot have a negative value, so, we take the result 2.

Final answer:

The smart-phone will hit the ground after approximately 3 seconds.

Explanation:

To find when the smart-phone will hit the ground, we need to determine the value of t that makes h equal to zero in the quadratic equation h = -16t^2 + 48t + 448. This equation represents the height h of the smart-phone after t seconds. To solve the equation, we can use the quadratic formula t = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values a = -16, b = 48, and c = 448, we can solve for t. The positive value of t will give us the time it takes for the smart-phone to hit the ground.

Step-by-step solution:

Substitute the values a = -16, b = 48, and c = 448 into the quadratic formula: t = (-48 ± sqrt(48^2 - 4*(-16)*448)) / (2*(-16))

Simplify the expression inside the square root: t = (-48 ± sqrt(2304 + 28672)) / (-32)

Simplify further: t = (-48 ± sqrt(30976)) / (-32)

Calculate the square root of 30976: t = (-48 ± 176) / (-32)

Determine the values of t: t = (-48 + 176) / (-32) = 3 or t = (-48 - 176) / (-32) = -5

Choose the positive value t = 3 since we are interested in the time it takes for the smart-phone to hit the ground

Therefore, the smart-phone will hit the ground after approximately 3 seconds.

Answer:

9

Step-by-step explanation:

We want to evaluate

[tex]A^2[/tex]

for A=-3.

This means, we need to substitute A=-2, into the given equation and simplify.

We substitute to get:

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

In this case the base is -3, so it multiplies itself twice.

[tex]A^2 = {( - 3)} \times - 3[/tex]

This gives us:

[tex]A^2 = 9[/tex]

Answer:

I need help with this too

Step-by-step explanation:

Answer: Xavier bought 2 apples and 9 bananas.

Step-by-step explanation:

Let x represent the number of apples that Javier bought.

Let y represent the number of bananas that Javier bought.

At the store, he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. This is expressed as

0.75x + 0.5y = 6 - - - - - - - - - - - - 1

He bought a total of 11 apples and bananas altogether. This means that

x + y = 11

Substituting x = 11 - y into equation 1, it becomes

0.75(11 - y) + 0.5y = 6

8.25 - 0.75y + 0.5y = 6

- 0.75y + 0.5y = 6 - 8.25

- 0.25y = - 2.25

y = - 2.25/ - 0.25

y = 9

x = 11 - y = 11 - 9

x = 2

Answer:

The probability that the customer must open 3 or more bottles before finding a prize is 0.64

Step-by-step explanation:

In order for a customer to have to open at least 3 bottles before winning a prize, then the first two bottles shouldnt have a price. The probability that a bottle doesnt have a price is 1-0.2 = 0.8. Since the bottles are independent from each other, then the probability that 2 bottles dont have a prize is 0.8² = 0.64. Therefore, the probability that the customer must open 3 or more bottles before finding a prize is 0.64

Answer:

We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.

Step-by-step explanation:

We know that the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next.

Therefore, we get p=0.2 and q=1-p=1-0.2=0.8.

So we will calculate the probability that the buyer will not win the prize in the first and second bottles. We get:

[tex]P=0.8\cdot0.8=0.64[/tex]

We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{small}{large}\qquad \qquad \stackrel{sides}{\cfrac{3}{7}} ~~ = ~~ \stackrel{areas}{\sqrt{\cfrac{A_1}{98}}}\implies \left( \cfrac{3}{7} \right)^2 = \cfrac{A_1}{98}\implies \cfrac{3^2}{7^2}= \cfrac{A_1}{98} \\\\\\ \cfrac{9}{49}= \cfrac{A_1}{98}\implies 882 = 49A_1\implies \cfrac{882}{49}=A_1\implies 18=A_1[/tex]

Answer:

The answer to your question is 18 in²

Step-by-step explanation:

Data

Big rectangle                  Small rectangle

Area = 98 in²                   Area = ?

Height = 7 in                    Height = 3 in

Process

1.- Calculate the base of the big rectangle

         Area = base x height

solve for base

         base = Area / height

substitution

          base = 98 / 7

          base = 14 ni

2.- Use proportions to find the base of the small rectangle

           x / 3 = 14 / 7

Simplify

          x = (14)(3) / 7

result

          x = 6 in                    

3.- Calculate the area of the small rectangle

          Area = 6  x 3

                   = 18 in²

Answer:

[tex]y=\frac{24}{x}[/tex]

Step-by-step explanation:

We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.  

We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of variation.

Upon substituting [tex]y=12[/tex] and [tex]x=2[/tex] in above equation, we will get:

[tex]12=\frac{k}{2}[/tex]

Let us solve for constant of variation.

[tex]12\cdot 2=\frac{k}{2}\cdot 2[/tex]

[tex]24=k[/tex]

Now, we will substitute [tex]k=12[/tex] in inversely proportion equation as:

[tex]y=\frac{24}{x}[/tex]

Therefore, the formula for the given scenario would be [tex]y=\frac{24}{x}[/tex].