Use the tangent to find the unknown side lengths.

Answer:

f(4) = 31

f(0) = 7

f(-1) = 1

Step-by-step explanation:

f(x) = 6x + 7

f(4) = 6(4) + 7

f(4) = 24 + 7

f(4) = 31

f(0) = 6(0) + 7

f(0) = 0 + 7

f(0) = 7

f(-1) = 6(-1) + 7

f(-1) = -6 + 7

f(-1) = 1

Answer:

The dimensions are 45 feet by 40 feet.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

[tex]\displaystyle A=w\ell[/tex]

Where w is the width and l is the length.

The length is five feet longer than the width. Thus, we can write that:

[tex]\ell = w+5[/tex]

The total area is 1800 square feet. Substitute:

[tex]1800=w(w+5)[/tex]

Solve for w. Distribute:

[tex]w^2+5w=1800[/tex]

Subtract 1800 from both sides:

[tex]w^2+5w-1800=0[/tex]

Factor. We can use 45 and -40. Hence:

[tex]\displaystyle (w+45)(w-40)=0[/tex]

Zero Product Property:

[tex]w+45=0\text{ or } w-40=0[/tex]

Solve for each case:

[tex]\displaystyle w=-45\text{ or } w=40[/tex]

Since the width cannot be negative, we can ignore the first solution.

So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.

The dimensions are 45 feet by 40 feet.

Answer:

B. (-r, 0)

Step-by-step explanation:

W is on the x axis, so the y coordinate is 0.

It is also r away from the origin, so the x coordinate is -r

Hope this helps!

Answer:

130 km/hr

Step-by-step explanation:

Average Speed = Total Distance / Total Time.

Let us just make up 2 distances from a time

A: 55 km/hour for 2 hours = 110 km

B: 75 km/hour for 2 hours = 150 km

Total Distance = 260 km

Total Time = 2 hours.

Average Speed = 260 / 2 = 130 km/hr

Now let's try it again. If we get a different answer, then the problem is unanswerable.

A: 55 km/hr  for 3 hours = 165 km

B: 75 km/hr for 3 hours = 225 km

Total distance  = 390 km

Total time = 3 hours

Average speed = 390 / 3 = 130 which is the same answer we got before.

9514 1404 393

Answer:

  y -9

Step-by-step explanation:

From 4 years ago until 5 years from now, John will age 9 years. That is, his age 4 years ago is 9 years less than it will be in 5 years.

John's age 4 years ago is y-9 years.

Answer:

Ok so these triangle are the same with equivalent angles

so we can add up the angles 80+26=106

now we subtract from 180

180-106=74

so the measure of angle b is 74

Hope This Helps!!!

her profit is 204 dollars and 68 cents= 204.68

Answer:

about 7.3 years

Step-by-step explanation:

[tex]8600=5000(1+\frac{.075}{4})^{4*t}\\1.72=(1.01875)^{4t}\\log_{1.01875}1.72=4t\\29.19428479=4t\\t=7.298571198[/tex]

Answer:

The answer is t=7.3

Answer:

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.

This means that [tex]p = 0.0746[/tex]

Random sample of 318 independent returns

This means that [tex]n = 318[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]

What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]

[tex]Z = -0.26[/tex]

[tex]Z = -0.26[/tex] has a p-value of 0.3974.

1 - 0.3974 = 0.6026

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Answer:

χ² = 4.80

Pvalue = 0.1874

Step-by-step explanation:

Given :

Category Observed (Expected)

A 25 (20)

B 35(40)

C 50(60)

D 90(80)

The Chisquare statistic (χ²) is given by :

χ² = Σ(observed - Expected)² / Expected

χ² = (25-20)²/20 + (35-40)/40 + (50-60)²/60 + (90-80)²/80

χ² = 1.25 + 0.625 + 1.67 + 1.25

χ² = 4.795

χ² = 4.80 (2 decimal places)

Using the Chisquare Pvalue calculator :

df = n - 1 = 4 - 1 = 3

Pvalue = 0.1874

Answer:

A) P(Type I error) = 0.045

B) P(Type II) error = 0.1

Step-by-step explanation:

We are told that the reliability of the test is 90% reliable.

Also, we are told that the probability that the test erroneously detects a lie even when the individual is actually telling the truth is 0.045.

Thus;

A) To calculate the probability of type I error:

From statistics, in this question we can say that the probability of a type I error is the probability that the test will erroneously detect a lie even though the individual is actually telling the truth. Thus;

Probability of (type I error) = P(rejecting true null) = 0.045

B) For probability of type II error, it is defined as the error where we accept a null hypothesis that is false. We can say that it produces a false negative and the formula is;

P(Type II) error = 1 - reliability

Reliability in the question is 0.90

Thus;

P(Type II) error = 1 - 0.9

P(Type II) error = 0.1

Answer:

perimeter=9cm

Area=2cm^2

step by step explanation:

Firstly solve the sides that don't have figures using trigonometry

#1..sin15°=opposite/hypotenuse

sin15=opposite/4

opposite=sin15×4

=1.035, round off to 1cm

Then find the value of the base

tan15=opposite/adjacent

tan15=1/adjacent

1=tan15adjascent

1/tan15=adjacent

adjacent or base=3.7 round off to 4cm

After finding these values find the perimeter

p=side+side+side

p=4cm+4cm+1cm

p=9cm

Find the area

1/2bh

1/2×4×1

A=2cm2

Answer:

Step-by-step explanation:

Solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is [tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

" Trigonometric ratios are defined as relation of the ratio of the sides of the triangle to the acute angle of the given triangle enclosed in it."

Formula used

[tex]cosec\theta = \frac{1}{sin\theta}[/tex]

According to the question,

Given trigonometric ratio equation,

[tex]\sqrt{3} (cosec\theta) -2=0[/tex]

Replace trigonometric ratio [tex]cosec\theta[/tex] by [tex]sin\theta[/tex]  in the above equation we get,

[tex]\sqrt{3} (\frac{1}{sin\theta} ) -2=0\\\\\implies \sqrt{3} (\frac{1}{sin\theta} ) = 2\\\\\implies sin\theta=\frac{\sqrt{3} }{2}[/tex]

As per given condition of the interval [ 0, 2π) we have,

[tex]\theta = sin^{-1} \frac{\sqrt{3} }{2} \\\\\ implies \theta = \frac{\pi }{3} or \frac{2\pi }{3}[/tex]

Hence, solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is

[tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

Learn more about trigonometric ratio here

https://brainly.com/question/1201366

#SPJ3

Answer:

DK = 10.23 units (approx)

Step-by-step explanation:

(DK * (CK + KE))/2 = 29

DK * CK = 29

180 - 31 = 149

149/2 = 74.5 --> degree of other angles

tan 74.5 = DK/CK

CK * tan 74.5 = DK

CK * CK * tan 74.5 = 29

CK = 2.83591462

2.83591462 * tan 74.5 = DK

DK = 10.22597776

So DK is approximately 10.23 units.

Hope this helps!

Answer:

P' (5, -4)

Step-by-step explanation:

P (4, -7)

x = 4 & Y =-7

T(4,. -7) = (4 + 1, -7 +3)

P' = (5, -4)

Answer:

You MADE IT EASY

Step-by-step explanation:

[tex] {y - 5 \times 9}^{2} \: times \: sevem \\ n \: equals \sec(x + {}^{2} ) [/tex]

Answer:

$15,540

Step-by-step explanation:

I DONT KNOW IF ITS RIGHT THO BUT

9% = 1,800

Answer:

i think you answer is correct as it has to be less that 64 yards since it is not on a big slant. using reference from the first section forty yards is not as big as the sectuon you are looking for therefore using estimation, the answer is most likely b 53 and 1 thirds

Answer:

A, C, D, F

Step-by-step explanation:

Given the expression : (3/5)³

Recall :

a^b where, a = base ; b = exponent

In ; (3/5)^3

Base = 3/5 ; exponent = 3

Similarly ;

a^b = a in b places

(3/5)^3 = (3/5) * (3/5) * (3/5)

(3/5) * (3/5) * (3/5) = (3*3*3) / (5*5*5) = 27/125

Hence, A, C, D and F are all correct

Answer:

Step-by-step explanation:

There are only 2 angle values  that <1 to <8 can be. The two values add up to 180

In this case <6 and <7 are equal.

<6 = 4x - 15

<7 = x + 30

4x - 15 = x + 30             Subtract x from both sides

4x-x - 15 = 30                Add 15 to both sides

3x = 30 + 15

3x = 45                         Divide by 3

x = 45 / 3                          

x = 15

<6 = 4x - 15

<6 = 4*15 - 15

<6 = 60 - 15

<6 = 45

Answer/Step-by-step explanation:

✔️-72 ÷ (-2)

The division of two negative numbers will give us a positive number. i.e. - ÷ - = +

Therefore:

-72 ÷ (-2) = 36

✔️-72 ÷ 2

The division of a negative number and a positive number will give us a negative number. i.e. - ÷ + = -

Therefore:

-72 ÷ 2 = -36

✔️72 ÷ (-2)

The division of a positive number and a negative number will give us a negative number. i.e. + ÷ - = -

Therefore:

72 ÷ (-2) = -36

Answer:

the answer to your question is B. 4 radians

9514 1404 393

Answer:

  p > 3

Step-by-step explanation:

  3p -4 -8p < -19 . . . . . . given

  -5p -4 < - 19 . . . . . . . . collect terms

  -5p < -15 . . . . . . . . . . . add 4

  p > 3 . . . . . . . . . . . . . . divide by -5 (reverses the inequality symbol)

Answer:

weak

Step-by-step explanation:

i dont be having fun at all

Answer:

7x = x + 9.

Step-by-step explanation:

7 × something = something + 9, right?

So, 7x = x + 9.

Answer:

-2, - 1, 0, 1, 2

Step-by-step explanation:

The greater than or equal to sign (≤) demonstrates that the unknown is equal to -2 and greater, but is less than 3, so the largest integer solution is 2, not 3