Consider the rectangle with width 20 in and length 26 in, write a ratio of the width to length

STEP - BY - STEP EXPLANATION

Whatto find?

• 90% confidence interval for the population proportion.

• 95% confidence interval for the ppulation proportion.

Given:

n= 800

p=0.66

q=1- p= 1- 0.66 =0.34

a) Given a 90% confidence interval,

α =1- 0.90= 0.10

b)

Given 95% confidence interal.

1- 0.95 =0.

ANSWER

a) (0.6276, 0.6324)

Is his answer reasonable: No, Emtiaz's answer is not reasonable because he assumed that the rate of descent was proportional.

The average rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Next, we would determine the rate at which the skydiver falls per seconds:

Rate = time/distance

Rate = 100/0.8

Rate = 125

Also, an equation which models the height (h) of the skydiver at a 0.8 seconds is given by:

h = 125t

At 3.1 seconds, we have:

Rate = time/distance

Rate = 500/3.1

Rate = 161.3

At 1.5 seconds, we have:

Rate = time/distance

Rate = 187.5/1.5

Rate = 125

Therefore, the average rate of change at each time interval is not equal and as such Emtiaz's answer is not reasonable because the rate increases as the time increases.

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The given parallelogram is a rhombus when x = 9 units

The parallelogram is a four sided plane with opposite sides parallel. So the opposite angles are equal. A parallelogram that has all angles are right angles is called rectangle.

The rhombus is a four sided plane with all of whose sides have the same length.

The sides are given,

9x-8 and 5x+28

In rhombus all the sides are equal

Then the equation will be

9x-8 = 5x+28

Rearrange the terms and solve it

9x-5x = 28+8

4x = 36

x = 36/4

x = 9

Hence, the given parallelogram is a rhombus when x = 9 units

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He spent $14.44 more on groceries this week than last week

From the question, the given parameters are

Amount spent last week = $58.34

Amount spent this week = $72.78

The additional amount that was spent at the grocery store this week is calculated by subtracting the amount spent this week from the amount spent last week

This is represented as

Additional amount = Amount spent this week - Amount spent last week

Substitute the known values in the above equation

So, we have

Additional amount = 72.78 - 58.34

Evaluate the difference

Additional amount = 14.44

Hence, an additional of $14.44 was this week

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The system of inequalities is 1.25x + 2y >= 375 and x + y <= 500, while the smallest number of chocolate covered almonds is 400

We make use of the following representations:

x = chocolate bars

y = chocolate covered almond

Using the above as a guide, and the given parameters;

We have:

1.25x + 2y >= 375 -- the amount raised

x + y <= 500 --- number of bars sold

From the question, we have

x = 100

Substitute x = 100 in x + y <= 500

100 + y <= 500

Evaluate

y <= 400

So, the least amount to sell is 400

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The probability that the customer came for lunch and did not order dessert is 7/113

The probability that the customer came for lunch or did not order dessert is 93/113

It is the chance of an event to occur from a number of possible outcomes.

It is given by:

Probability = Number of required events / Total number of outcomes

We have,

Total number of customers = 113

             Desert      Non desert

Lunch     7               1 3

Dinner    30             63

The probability that the customer came for lunch and did not order dessert:

= 7 / 113

The probability that the customer came for lunch or did not order dessert:

= (7+13)/113 + (13 + 63)/113

= 20/113 + 73/113

= 93/113

Thus,

The probability that the customer came for lunch and did not order dessert is 7/113

The probability that the customer came for lunch or did not order dessert is 93/113

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The distance between the points (−3, −5) and (−3, −7) is 2 units.

The distance formula gives the shortest distance between two points in a two-dimensional plane.

The distance formula is a useful tool for calculating the distance between two points.

Therefore,

d = √(x₂ - x₁)²+(y₂ - y₁)²

Let's find the distance between the points (−3, −5) and (−3, −7).

Hence,

x₁ = -3

x₂ = -3

y₁ = -5

y₂ = -7

d = √(-3 + 3)² + (-7 + 5)²

d = √(-2)²

d = √4

d = 2

Therefore, the distance between the point is 2 units.

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Given:

Here the system of eqution is given as

Required:

Solve using the substitution method

Explanaton:

First put

in

we get

now isolate x

now put the value of x first equation

Final answer:

Solution of given system of equation by using elimination is

EXPLANATION

Let's see the facts:

Heights of 8th grade boys ---------------> Normally distributed

Mean= 50 inches

Standard deviation= 4 inches

d) Probability that boy shorter than 56 inches:

x=56

P(x<56)

We know that z-score=

Replacing terms:

P-value from Z-table =

P(x<56) = 0.93319

Answer: The probability that an 8th grade boy will be shorter than 56 inches is 0.93319*100= 93.3%.

c) Percentage of 8th grade boys that are between 56 and and 60 inches tall is:

P-value from Z-table =

P(x<60) = 0.93319

P-value from Z-table =

P(x<60) = 0.99379

Then, subtracting both probabilities.

P(56

Answer: the percentage of 8th grade boys that are between 56 and 60 inches tall is 0.0606*100 = 6.06%.

a) We have that,

According to the Empirical Rule, we can assevere that 50+- 3σ = 50+- 3*4 ---->

50 + 12 = 62 inches

50 - 12 = 38 inches

About 99.7% of 8th grade boys height will fall between 38 inches and 62 inches.

Answer: Approximately 99.7% of the heights fall between 38 inches and 62 inches.

b) According to the Empirical Rule, we can assevere that around 68% of the data will fall within one standard deviation of the mean. As we already know, the standard deviation σ is a natural yardstick for any measurements that follow a normal distribution.

So, 50 +- σ = 50 +- 4 ---->

50 + σ = 50 + 4 = 54

50 - σ = 50 - 4 = 46

Answer: About 68% of 8th grade boys height will fall between 46 inches and 54 inches.

x³ is N²/15. The index form of a number is that digit written as an exponential expression or an unmarried number presented to another number.

A number's index form is that number written as an exponential expression or as a single number raised to another number. The exponent, or index, of an exponential expression indicates how many times the base must be multiplied by itself to evaluate the expression.

This fact can be used to write a number in index form. An index number is a number that has been multiplied by a power. The power, also known as the index, indicates how many times the number must be multiplied by itself. For example, 25 means multiplying 2 by itself five times

= 222222 = 32. There are several important index number rules:

ya × yb = y.

Therefore,

[tex]$x^3=\frac{N^2}{15}[/tex]

For [tex]$x^3=f(a)$[/tex] the solutions are

[tex]$x=\sqrt[3]{f(a)}, \sqrt[3]{f(a)} \frac{-1-\sqrt{3} i}{2}, \sqrt[3]{f(a)} \frac{-1+\sqrt{3} i}{2}$$$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2},[/tex][tex]$x=\sqrt[3]{\frac{N^2}{15}} \frac{-1-\sqrt{3} i}{2}$$[/tex]

Simplify

[tex]$\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2}: \quad-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}-\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x^3=\frac{N^2}{15}[/tex]

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Solution:

Given:

The dinner bill = $21.00

The tip = 15% of the bill

Hence,

Therefore, the tip will be $3.15

The solution of the equation for t is t = i/pr

The equation is given as

i = prt

Divide both sides of the equation by p

So, we have the following equation

i/p = prt/p

Divide both sides of the equation by r

So, we have the following equation

i/pr = prt/pr

Evaluate the quotients

i/pr = t

Rewrite as

t = i/pr

By the above computation, we changed the subject of the formula in i = prt from i to t.

This implies that solving for t is a concept of subject of formula

Hence, the solution is t = i/pr

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Multiply the numbers and combine exponents with the same base.

Lisa's car gets 31 miles per gallon.

Thus in 22 gallons she can drive,

22x31=682 miles.

Lisa can drive 682 miles.

The height of the ball at a horizontal distance of R meters from Kaori is H(R)=4H.

Kaori taking a free throw is a guarantee. H(d) simulates the basketball's height (in meters) at d meters of horizontal separation from Kaori.

It is said that H(R) = 4H.

In this case, H(R) displays the height of a basketball instead of H(d). Therefore, it is evident that a basketball's height is 4H since H(R)=4H at d = R.

The horizontal distance from Kaori is R because d is the horizontal distance from Kaori.

Thus the height of the ball is 4H meters at a horizontal distance of R meters from Kaori, according to the expression H(R)=4H.

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The actual distance between the golf vein and the farthest gold dust strike is; 79 miles.

It follows from the task content that the actual distance between both locations is to be determined.

It follows from the distance formula in coordinates geometry that;

D = √{(x2 - x1)² + (y2 - y1)²}

Therefore, the distance between the gold vein and the farthest gold dust strike is;

D = √{(-9 -(-9))² + (71 - (-8))²}

D = √79²

D = 79.

Ultimately, the distance on the graph is 79 units and since each unit on the.graoh represents 1 mile, the actual distance between the gold vein and the farthest gold dust strike is; 79 miles.

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We must write the ratio 7 to 15 and reduce it to the lowest term if possible.

The ratio is:

Because 15 is not divisible by 7, we conclude that the ratio is already in its lowest form.

7+14m

Explanation

Step 1

Let

m represents Marbel's age

Then,

the product of 14 and Mabel's age=

now, Seven more than the product of 14 and Mabel's age

then

Step 1:

Write the equation

Step 2:

Express the equation in exponential form

Final answer

x = 4

Answer:

4

Step-by-step explanation:

put in equation form

7x - 12 = 16

solve for x

7x = 28

x = 4

Solution:

Scott paid;

$13.24 for 3.41-pound bag of shrimp

This means,

$18.99 for 4.96-pound bag of shrimp

This means,

Therefore, the bag that is a better buy based on the unit price is the 4.96-pound because of the unit price which is lesser than the unit price for the 3.41-pound bag.

Thus, the 4.96-pound is a better buy.

From cosecant identity the expression cos(x)+sin(x)/ sin(x) =1+cot(x) was verified.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) ,  cos  (x) and tan  (x) , where:

sin (x) = [tex]\frac{opposite\ leg}{hypotenuse}[/tex]

cos(x)=[tex]\frac{adjacent\ leg}{hypotenuse}[/tex]

tan (x) = [tex]\frac{\frac{opposite\ leg}{hypotenuse} }{\frac{adjacent\ leg}{hypotenuse} } = \frac{opposite\ leg}{adjacent\ leg}[/tex]

The question gives the following identity:  [tex]\frac{cos (x)+sin(x)}{sin(x)}[/tex]

First, you should rewrite the identity using the cosecant  identity -                          csc(x)= 1/sin(x) . Then,

(cos(x)+sin(x)) * csc(x)

After that, you should expand the previous expression.

cos(x)*csc(x) + sin(x)  * csc(x)

cos(x)*1/sin(x) + sin(x)  * 1/sin(x)

cos(x)/sin(x) + sin(x)/sin(x)

cot(x) + 1

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x³+2x²+4x+8=0

Rearrange

x³ + 4x + 2x²+ 8 = 0

x ( x² + 4 ) + 2( x² + 4) = 0

(x + 2) ( x² + 4) = 0

The factors are;

(x + 2) (x² + 4)

(x²+ 4) can further be simplified to give (x- 2i) (x + 2i)

The contrapositive of the statement is:

Jose isn't going for a bike ride if and only if he doesn't woke up early.

What is contrapositive?

A conditional statement's hypothesis and conclusion are switched, and both are then rejected, in a contrapositive. For instance, "if not B then not A" is the opposite of "if A then B." A conditional statement's contrapositive combines the inverse and converse.

The given statement is,

Jose wakes up early if and only if he is going for a bike ride.

We divide the statement into two parts.

1. Jose wakes up early.

2. He is going for a bike ride.

The negative of the statements are,

Jose doesn't wakes up early and he isn't going for a bike ride.

Therefore, the contrapositive of the statement is,

Jose isn't going for a bike ride if and only if he doesn't woke up early.

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Answer:

175,760,000

Step-by-step explanation:

This is the counting principle.

There are 7 positions. Multiply the number of possible characters in each position.

_ × _ × _ × _ × _ × _ × _

The numbers are from 0 to 9, so there are 10 of them.

There are 26 letters in the English alphabet.

10 × 10 × 26 × 26 × 26 × 10 × 10

Answer: 175,760,000

ANSWER:

B. Similar - SAS

EXPLANATION:

Given:

Recall that the SAS Similarity Rule states that if two sides of one triangle are proportional to two corresponding sides of another triangle and the included angle in both triangles are congruent, then the two triangles are said to be similar.

Looking at triangles ABC and DEF, we can see that, we can see that;

Since the two corresponding sides of both triangles are in equal proportion and the included angle in both triangles are congruent, then triangles ABC and DEF are similar by the SAS Similarity Rule

To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.

What is coordinate geometry?

The science of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry).

Finding the difference between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

m=(rise/run) = (y2-y1)/(x2-x1)

(x1,y1) =  coordinates of the line's first point

(x2,y2) = coordinates of the line's second point

To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.

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Given:

Find: Area of the figure.

Sol:

The area of Triangle ABH is:

Area

In triangle is:

Base = (9-3)

Height = 8

So Area of ABH is:

Area of rectangle BDFH so,

Width = 8

We have to estimate how much he expects to make investing $4200 if he should make $12 for every $100.

We can apply the rule of three as:

Answer: he expects to make $504.

Answer:

These points are mine :)))

Step-by-step explanation: