In ΔPQR, \overline{PR} PR is extended through point R to point S, \text{m}\angle QRS = (7x+8)^{\circ}m∠QRS=(7x+8) ∘ , \text{m}\angle RPQ = (x+12)^{\circ}m∠RPQ=(x+12) ∘ , and \text{m}\angle PQR = (3x+20)^{\circ}m∠PQR=(3x+20) ∘ . Find \text{m}\angle RPQ.m∠RPQ.

Answer:

x=60

Step-by-step explanation:

these shapes seem to be flipped

side WZ seems to be similar to PS

and Side ZY seems to be similar to RS

ewe can make ratios on the side lengths

40/75=32/x

cross multiply

40x=75(32)

40x=2400

/40.  /40

x= 60

hopes this helps please mark brainliest

Answer:

Answer Option C: SSA

Answer: lines j and k are perpendicular

Step-by-step explanation:

Let's find the equations of lines j and k

                       [tex]\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

Line j: (8,2)  (-2,-2)

x₁= 8     x₂=-2    y₁=2     y₂=-2

[tex]\displaystyle\\\frac{x-8}{-2-8}=\frac{y-2}{-2-2} \\\\\frac{x-8}{-10}=\frac{y-2}{-4} \\\\[/tex]

 Multiply both parts of the equation by -4:

[tex]\displaystyle\\\frac{2}{5} (x-8)=y-2\\\\\frac{2}{5} x-\frac{16}{5} =y-2\\\\\frac{2}{5} x-3.2+2=y-2+2\\\\\frac{2}{5}x-1.2=y\\\\ Thus,\ y=\frac{2}{5}x-1.2[/tex]

Line k: (-4,3)   (-6,8)

x₁=-4    x₂=-6    y₁=3    y₂=8

[tex]\displaystyle\\\frac{x-(-4)}{-6-(-4)} =\frac{y-3}{8-3} \\\\\frac{x+4}{-6+4}=\frac{y-3}{5} \\\\\frac{x+4}{-2} =\frac{y-3}{5}[/tex]

Multiply both parts of the equation by 5:

[tex]\displaystyle\\-\frac{5}{2}(x+4)=y-3\\\\ -\frac{5}{2}x-10=y-3\\\\ -\frac{5}{2}x-10+3=y-3+3\\ -\frac{5}{2}x-7=y\\Thus,\ y=-\frac{5}{2} x-7[/tex]

Hence, lines j and k are perpendicular

We can conclude that there is a statistically significant correlation between the two variables, a and b. The correlation coefficient is .10, which indicates a weak positive relationship.

A correlation coefficient of .10 indicates that there is a weak positive relationship between the two variables, a and b. A p-value of .01 indicates that the correlation between the two variables is statistically significant, meaning that it is unlikely to be due to chance. This suggests that there is a real relationship between the two variables, even though it is weak.

To calculate the correlation coefficient, you can use the formula  where x and y are the two variables in question. In this case, the correlation coefficient is .10. This can be determined by plugging in the values for x and y and doing the necessary calculations.

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The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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Answer: (4, 10)

Step-by-step explanation:

The first number, 4, is the number on the x axis, the horizontal axis. The second number 0 is the number on the y axis, the vertical axis.

If you move up you would moving on the y axis, therefore the second number, 0, would change.

You moved 10 units so starting at 0 move up 10 units. 0 + 10 = 10

Now you're at (4, 10)

Answer: 11.64%

Step-by-step explanation:

The number of tickets they purchased is 4.

The expression that would b used to represent the total cost at the carnival is a linear expression. A linear expression is an expression that has a single variable that is raised to the power of one.

The form of the linear expressions that can be used to represent the total cost at the carnival is:

Total cost = admission fee + (price per ride x number of rides)

Total cost in option 1 = $5 + 0.30r

Total cost in option 2 = $3 + $0.80r

Where r = number of rides

When they pay the same amount of money, the linear functions would be equal:

$5 + 0.30r = $3 + $0.80r

$5 - $3 = $0.80r - 0.30r

$2 = $0.50r

r = 2 / 0.5

r = 4

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Answer: -1/28 gallon

Step-by-step explanation:

divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)

Answer: -1/28 gallon

Step-by-step explanation:

Answer:

n = 4

Step-by-step explanation:

Given equation:

[tex]\sqrt[3]{y^2} =\sqrt[6]{x}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies y^{\frac{2}{3}}=x^{\frac{1}{6}[/tex]

Take both sides of the equation to the power of ³/₂:

[tex]\implies \left(y^{\frac{2}{3}}\right)^\frac{3}{2} =\left(x^{\frac{1}{6}\right)^\frac{3}{2}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies y^{\frac{2}{3} \cdot \frac{3}{2}}=x^{\frac{1}{6} \cdot \frac{3}{2}}[/tex]

Simplify:

[tex]\implies y^{\frac{6}{6}}=x^{\frac{3}{12}[/tex]

[tex]\implies y^1=x^{\frac{1}{4}[/tex]

Apply exponent rule  a¹ = a :

[tex]\implies y=x^{\frac{1}{4}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies y=\sqrt[4]{x}[/tex]

The length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

A quadrilateral with at least one set of parallel sides is called a trapezoid in American and Canadian English.

In British and other varieties of English, it is termed a trapezium.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The parallel sides are called the basis of the trapezoid.

So, we have:
The height should be 3 yards higher than the shorter base.

b₁=h+3

The height should be 3 yards higher than the shorter base.

b₂=h+7

Formula for Area of trapezoid = 1/2(b₁+b₂)h

Now, using the formula, calculate as follows:

150=1/2(h+3+h+7)h

150=(2h+10)h/2

150=2h²+10h/2

150=2h²+5h

h²+5h-150=0

h²+15h-10h-150=0

h(h+15)-10(h+15)=0

(h-10)(h+15)=0

h=10 or h-15

h should be positive:

b₁=h+3=15+3=18

b₂=h+7=15+7=22

Therefore, the length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

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Complete question:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be

In the given formula we have variables:

If we have to solve it for P then it should be called 'Principal' or 'Loan amount'.

If we have to solve it for n then it should be called 'Number of payments' or 'Number of installments'.

Since n is the power of a number we need logarithm to solve it for n.

Answer:

"Principal (loan amount)"

"Term of the loan (in months)" or "Number of monthly payments"

Logarithms

Step-by-step explanation:

Monthly Payment Formula

[tex]M=\dfrac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}[/tex]

where:

If we solve for P, the name of the formula is "Principal (loan amount)".

If we solve for n, the name of the formula is "Term of the loan (in months)" or "Number of monthly payments".

When solving for n, we need to use logarithms:

[tex]\boxed{\begin{aligned}M&=\frac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\\\\M(\left(1+r\right)^n-1)&=Pr\left(1+r\right)^n\\\\\frac{\left(1+r\right)^n-1}{\left(1+r\right)^n}&=\frac{Pr}{M}\\\\1-\frac{1}{\left(r+1\right)^n}&=\frac{Pr}{M}\\\\\frac{1}{\left(r+1\right)^n}&=1-\frac{Pr}{M}\\\\\left(r+1\right)^{-n}&=1-\frac{Pr}{M}\\\\\ln \left(r+1\right)^{-n}&=\ln \left(1-\frac{Pr}{M}\right)\\\\-n\ln(r+1)&=\ln\left(1-\frac{Pr}{M}\right)\\\\n&=\frac{-\ln\left(1-\frac{Pr}{M}\right)}{\ln(r+1)}\end{aligned}}[/tex]

Answer:

10 yrs old and 35 yrs old

Step-by-step explanation:

I figured it out by trial and error but here's the thinking process.

10 + 35= 45

Son becomes dad's age so 35-10=25, so plus 25 year to each age.

10+25=35

35+25= 60

35+60=95

I hope that makes enough sense!

The slope-intercept form of the equation 8x = 4y + 16 will be y = 2x -4.

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The equation given is 8x = 4y + 16.

We must solve for y as follows;

8x = 4y + 16

4y = 8x -16

By dividing through by 4; we have;

y = 2x -16

Hence the equation for both lines will be y = x +3 and   y  = x+13

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The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.

On data that is dispersed normally, the Z test is a parametric process that is applied. The z-test can be applied to proportions, two samples, or one sample to test hypotheses. When the population variance is known, it is possible to determine whether the means of two significant groups differ.

The second is one-way analysis of variance (ANOVA), which checks if three or more samples originate from populations with the same mean using the F-distribution.

The test statistic should be compared to the crucial value. If the test statistic is more extreme in favor of the alternative than the crucial value, the alternative hypothesis should be considered instead of the null hypothesis. If the test statistic is not as extreme as the crucial value, the null hypothesis should not be disregarded.

Therefore,

The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.

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The possible number of hours Henry could trim trees is t > 10.

The given information represents a scenario which demonstrates an inequality statement as Henry wants to earn at least $ 56, which means the amount earned should be greater than 56.

Let t be the possible number of hours Henry trim trees. As his per hour charge is $6 and he pays $4 in equipment fee, the inequality statement is:

6t – 4 > 56

Solving,

6t  > 56 + 4

6t  > 60

t > 10.

In order to earn at least $56, Henry must trim trees for at least 10 hours or more.

Note: The question is incomplete. The complete question probably is: Henry wants to earn more than $56 trimming trees. He charges $6 per hour and pays $4 in equipment rental fees. What are the possible number of hours Henry could trim trees?

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Answer:

the height of the goalpost is approximately 10.48 meters.

Step-by-step explanation:

To find the height of the goalpost, Addison needs to use the distance from the mirror to the goalpost, the distance from her eyes to the ground, and the angle formed by the goalpost, the mirror, and her eyes. She can use the law of cosines to solve for the height of the goalpost.

Let "a" be the distance from the goalpost to the mirror, "b" be the distance from the mirror to Addison's eyes, and "c" be the distance from Addison's eyes to the ground.

The law of cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle formed by the goalpost, the mirror, and Addison's eyes.

In this case, a = 13.25 meters, b = 1.3 meters, and c = 1.55 meters. We can substitute these values into the formula to solve for the angle C:

1.55^2 = 13.25^2 + 1.3^2 - 2 * 13.25 * 1.3 * cos(C)

Solving for cos(C) and using the inverse cosine function (arccos), we find that C = 52.22 degrees.

Now that we know the angle C, we can use the law of sines to solve for the height of the goalpost. The law of sines states that:

sin(C) / a = sin(A) / h, where A is the angle formed by the ground, the mirror, and the goalpost, and h is the height of the goalpost.

In this case, A = 180 - C - 90 = 180 - 52.22 - 90 = 37.78 degrees, and a = 13.25 meters. We can substitute these values into the formula to solve for h:

sin(52.22) / 13.25 = sin(37.78) / h

Solving for h, we find that the height of the goalpost is approximately 10.48 meters.

Therefore, the height of the goalpost is approximately 10.48 meters.

The rate at which Submarine B descends is 29.8 feet per hour.

The rate refers to the average speed of an object in motion from one point to another.

The rate can be determined by dividing the distance by the time.

The rate or average speed is the quotient between distance and time.

The distance descended by Submarine A = 193.5 feet (126 + 4 ½ x 15)

The time Submarine B descends = 6.5 hours

Submarine B's rate of descent = 29.77 feet (193.5/6.5) per hour

= 29.8 feet

Thus, we can conclude that Submarine B descends at the rate of 29.8 feet every hour, whereas, Submarine A descends 15 feet per hour.

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Answer: 67/15

Step-by-step explanation:

-3+7x-9+8x=54

-12 + 15x = 54

15x = 67

x = 67/15

The required choice for inequality is Option 2.

What is inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

Given, 3(8 – 4x) < 6(x – 5)

or, 24 - 12x < 6x - 30

or, 24 + 30 < 6x + 12x

or, 54 < 18x

or, 18x > 54

or, x > 3 means x is greater than positive 3 and pointing to the right.

Hence, the required choice for inequality is Option 2.

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Answer: b

Step-by-step explanation:

You determine the limit by [tex]\lim_{n \to \infty} a_n = -1[/tex].

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. The concept of limit, which is founded on the idea of closeness, is largely used to give values to some functions at points when none are defined in a way that is consistent with values close by.

Divide the denominator and numerator by 3n as shown.

[tex]\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{2^n+3^n}{2^n-3^n\\}[/tex]

[tex]= \lim_{n \to \infty} \frac{(\frac{2}{3})^n+1 }{(\frac{2}{3})^n-1 } \\=\frac{0+1}{0-1} \\=-1[/tex]

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The probability that there is at least two 4s in the three throws is 0.05 or 5%

Probability

In statistics, probability deals with the possibility of happening of the events.

Given,

Here we know that the throw a fair die three times. if we observe the first throw is a 4.

And we need to find the probability that there is at least two 4s in the three throws.

According to the given question, we know that the dice is thrown 3 time.

Then the sample space of the given event is 216.

Here we know that the first throw has 4.

And we need to find the probability of getting two 4s in the 3 throws,

So, the possible number of events are.

=> {444, 441, 442, 443, 445, 446, 414, 424, 434, 454, 464}

So, the total possible number is 11.

Then the probability is,

=> 11/216

=> 0.05 or 5%

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If the raisin swells to twice its original size, relative to the water, the raisin must have been a)hypertonic solution. So, correct option is a.

Hypertonic alludes to an answer with higher osmotic strain than another arrangement. At the end of the day, a hypertonic arrangement is one in which there is a more noteworthy fixation or number of solute particles outside a layer than there are inside it.

Hence, correct option is a.

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(Complete question) is:

You are bored at a lunch meeting and surreptitiously place a raisin in your glass of iced tea. The raisin shrinks to half its original size. The raisin must have been a __?__ solution.

a)hypertonic

b)aquatonic

c)hypotonic

d)isotonic

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+160}x\stackrel{\stackrel{c}{\downarrow }}{+20} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 160}{2(-16)}~~~~ ,~~~~ 20-\cfrac{ (160)^2}{4(-16)}\right) \implies \left( - \cfrac{ 160 }{ -32 }~~,~~20 - \cfrac{ 25600 }{ -64 } \right) \\\\\\ \left( 5 ~~~~ ,~~~~ 20 +400 \right)\implies (\stackrel{seconds}{5}~~,~~\stackrel{feet}{420})[/tex]

Answer:

Substitute x = 4 into the equation.

f(4) = 2(4)² - 6

= 2(16) - 6

= 32 - 6

= 26

If Marcus monthly salary is $1,500 plus 10% of sale, then he could earn 1500 + 0.09x per month with salary and 9% sales

Monthly salary of Marcus = $1500

The percentage incentives for sales = 10%

If the percentage of incentive for sales is 9 %

Consider the amount of sales is $x

Therefore the monthly salary of Marcus = Monthly salary of Marcus + (The amount of sales × 9/100)

Substitute the values in the equation

The monthly salary of Marcus = 1500 + (x×9/100)

Divide the numbers in the equation

= 1500 + (x × 0.09)

Multiply the numbers the numbers

= 1500 + 0.09x

Therefore, the monthly salary of Marcus will be 1500 + 0.09x

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The chance density characteristic of lifetime in months of a transistor in a positive utility is:

[tex]f(x)=0.4cdot e^x > 0f(x)=0.4⋅e −0.4x ;x>0[/tex]

The chance density characteristic shows that the random variable X follows a exponential characteristic with parameter λ = 0.4.

Compute the suggest lifetime as follows:

[tex]mu=frac=2.5μ= λ1 = 0.401 =2.5[/tex]

Thus, the suggest lifetime is months.

Compute the usual deviation of the lifetimes as follows:

[tex]sigma=2.5σ= λ 2 1 = 0.40 2 1 =2.5.[/tex]

Thus, the usual deviation of the lifetimes is 2.5 months.

Compute the sixtieth percentile of the lifetime as follows:

Thus, the sixtieth percentile of the lifetime is 2.3 months.

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Fron the given question, we can say that systematic sample because not all sample are possible.

Using the probabilistic sampling technique known as systematic sampling, researchers periodically choose individuals from a community. Choose each 15th of her, for instance, from the population list. You can simulate the advantages of straightforward random sampling by randomly sorting the population.

[tex]Since every 100th horse is selected in the sample. Thus, Systematic Sampling is used.[/tex]

Further,

Sampling method is said to be Simple Random Sampling if unit from the population are picked randomly without any criteria, so that each unit as similar chance of selection.

If any criteria are used to select every sample, such as selecting every fourth unit, the sampling technique is said to be systematic sampling.

If the population is divided into various groups that share the same characteristic, the sampling method is said to be stratified sampling. Additionally, units are chosen at random from these groups.

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Answer:

Step-by-step explanation:

We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:24⋅2−2=24⋅12+2=244=6

Answer:

We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:

24⋅2−2= 24⋅1/2 OVER +2= 24/4= 6

Step-by-step explanation: