the largest interior angle in an isosceles trapezoid is 4 times the measure of the smallest interior angle. what is the measure, in degrees, of the smallest interior angle in the trapezoid?

Answer:

d: y=5x

Step-by-step explanation:

Since we know a few points: (2,10), (3,15), (4,20), we can use two of them to first find the slope. The equation for the slope is (Increase in y)/(increase in x).

1. Slope between (2,10) and (3,15) is 5/1 which is 5. So the slope will be 5.

2. With the slope, we know that our equation will be: y=5x+b. To find b, we can replace x and y with another point. 20 = 5(4)+b. --> 20 = 20 +b. Now we know that b equals 0.

Our final equation will be y = 5x.

RECHECKING!

I'll recheck whether my answer is right or not using Desmos (A online graphing calculator).

I added an image down below, and I drew the points in blue. This shows that since the graph crosses all three points, it is correct.

WHY y=1/5x IS NOT CORRECT (based on your comments)

If you look at the points, the relationship between x and y is not 1/5. If you multiply something from x, it should become 10.

--> 2 times __ = 10

--> 3 times __ = 15

--> 4 times __ = 20

And clearly, __ will be 5. If it becomes 1/5, we won't get the right number of y.

This is why y=1/5 is not correct.

Hope this helps!

Answer: 23/26

Step-by-step explanation:

Let’s say we have 3 spots, one for each of the three exchange students. It doesn’t matter who goes with who, we’re just going to choose people.

If LaQuinta is NOT one of the people chosen, then there are 25 possible people left to become tour guides. We will need to choose 3 of them, so there are (25 choose 3) = 2,300 ways.

With no restrictions, there are 26 people to choose from and 3 spots to fill. Therefore there are (26 choose 3) = 2,600 ways to fill these 3 spots with no restrictions.

The total probability is 2,300/2,600, which simplifies to 23/26.

A = 6 cm; B = 3 cm; C = 8 cm; D = 10 cm

The Surface area of the prism = 120 cm².

Surface area = Area of A + B + C + D

The side lengths are:

A = 6 cm

B = 3 cm

C = 8 cm

D = 10 cm

Surface area of the prism = 2(area of triangular face) + area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Area of triangular face = 1/2(b)(h) = 1/2(8)(6) = 24 cm

Area of rectangle 1 = (length)(width) = (10)(3) = 30 cm²

Area of rectangle 2 = (length)(width) = (6)(3) = 18 cm²

Area of rectangle 3 = (length)(width) = (8)(3) = 24 cm²

Surface area of the prism = 2(24) + 30 + 18 + 24 = 120 cm².

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Answer:

5:9

Step-by-step explanation:

So since 18 chose to do oral report, that means (28-18) or 10 students decided to do a written report.

To find the written to oral report ration, we need to find for each student that did a written report, how many did an oral report? We can express this as a fraction and simplify to get the simplified ratio. So the the written will be the numerator and the oral will be the denominator: 10/18, to simplify this simply divide both sides by 2, to get 5/9 which gives us the simplified ratio of 5:9 meaning that for every 5 students who decided to do a written report 9 students decided to do an oral report.

What is inequality?

In Algebra, inequality shows the relation between two expressions using the inequality symbol.

The graph shows the equation y<x^2+1 is attached

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The graph at option 1 shows the given inequality y < x² + 1. The domain and range of the given inequality is {x: x ∈ (-∞, ∞)} and {y: y ∈ [1, ∞)}.

The steps to graph an inequality equation are:

The given inequality is y < x² + 1

Finding points to graph the boundary line by taking y = x² + 1:

When x = -2,

y = (-2)² + 1 = 4 + 1 = 5

⇒ (-2, 5)

When x = -1,

y = (-1)² + 1 = 2

⇒ (-1, 2)

When x = 0,

y = (0)² + 1 = 1

⇒ (0, 1)

When x = 1,

y = (1)² + 1 = 2

⇒ (1, 2)

When x = 2,

y = (2)² + 1 = 5

⇒ (2, 5)

Plotting these points in the graph forms an upward-facing parabola.

So, all the points above the vertex of the parabola satisfy the given inequality. Thus, that part is shaded.

From this, the graph at option 1 is the required graph for the inequality y < x² + 1. The boundary line is dashed since the inequality symbol is " < ".

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Answer:

Hi, I'm not for sure but I think for sure for the answer is, I haven't done this math in a while btw I like math lol, but I will try my best for this answer:

The quotient:   x + 4

The remainder: - 2

Step-by-step explanation:

I hope this helps you and have a lovely day of learning!

Answer:

option A. is the midpoint of the graph

The probability would be 3/125 in the given conditions.

As there are 105 items, of which 30 are bats. The probability for that draw is 30/105.

There are now 104 items remaining, of which 15 are gloves. The probability of getting a glove now is 15/104.

There are now 103 items remaining, of which 60 are balls. The probability of getting a ball now is 60/103.

The probability of all three occurring = product of three

15/104* 30/105* 60/103

= 3/125

Hence the probability is 3/125.

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The statements that are true for the box plots are:

C. The median of Nadia’s data = median of Ben’s data.

D. Nadia had the highest score on a test

The median of a data set is the center value, which is indicated on a box plot by a vertical line that divides the box.

Given the two box plots, we can conclude that:

Median for the data of Nadia is 92, which is the same for Ben.

The extreme whisker to the right for Nadia is at 100, which is the highest value for Nadia while that of Ben is 99.

The true statements are:

C. The median of Nadia’s data = median of Ben’s data.

D. Nadia had the highest score on a test

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Answer:

"C" and "D"

Step-by-step explanation:

took test on edge 2023

The ratio between the circle and triangle is described as 3:4.

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Answer:

98

Step-by-step explanation:

m<KJU + m<UJI = m<KJI

this equation will help us find the value of x therefore the value of m<KJU

Rewrite the equation using the expressions

104 + x + x + 76 = 168 add like terms

180 + 2x = 168 subtract 180 from both sides

2x = -12 divide both sides by 2

x = -6 to find the value of m<KJU replace x with -6

104 + (-6) = 98

The correct values for a and b which models this relationship through an exponential function are 8 and 2 respectively.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = eˣ

Based on the information provided, we can logically deduce that the other copy machine can reduce image dimensions by a different percentage and this is defined by the following exponential function:

f(x) = abˣ

From the graph (see attachment), we have;

When x = 0, y = f(x) = 8. Thus, f(0) = 8

f(x) = abˣ

8 = ab⁰

8 = a × 1

a = 8.

Also, from the graph (see attachment), we have;

When x = 1, y = f(x) = 4

f(x) = abˣ

4 = 8b¹

4 = 8 × b

4 = 8b.

b = 8/4

b = 2.

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Answer:

h (1) = $140

Step-by-step explanation:

10x + 150

-10     -10

150-10

=140

so the answer must be $140

So it is definitely the first one

H(12)=$270

The width of the delivery box is 9 inches.

Given that  volume of delivery box is 756 cubic inches,length is 6 inches less than twice the width, height is 2 inches less than width.

let width be x

Length = 2x- 6

Height = x - 2

Width = x

We can find the value of x by putting values one by one and then we will be able to get the value of  x which is width.

Because the delivery box is cuboid in shape so the volume is equal to product of length,breadth and height.

When x=7: Volume=7 x (7 - 2) x (2x7 - 6) = 7 x 5 x 8 = 280

When x=9,Volume will be 9 x (9 - 2) x (2x9 - 6) = 9 x 7 x 12 = 756

Therefore, the width of the delivery box is 9 inches.

Hence the width of the delivery box is 9 inches.

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In light of the provided confidence interval, the following is the best answer on the outcome of the hypothesis test:

Yes, because 0 is not in the confidence interval.

[tex]$H_{0}: \mu=0$[/tex]

[tex]$H_{1}: \mu \neq 0$[/tex]

yes, because 0 is not in the confidence interval

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Given the 6 pound weight of the new seasoning having ingredients that cost $8, and $11, the amount she should charge for 1 ounce is $0.53125

The ingredients in the new seasoning are;

5 pounds of dried rose hips + 1 pounds of five-spice powder

Cost of the ingredients are;

1 pound of dried rose hips = $8

1 pound of five-spice powder = $11

The cost of combined spice, C, is therefore;

C = $8 × 5 + $11 × 1 = $51

The weight of the new combined seasoning = (5 + 1) pounds = 6 pounds

Cost of 1 pound of the new seasoning is therefore;

[tex]1 \: lb = \frac{51}{6} = 8.5[/tex]

Therefore;

[tex]1 \: ounce = \frac{8.5}{16} = \mathbf{0.53125}[/tex]

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Answer: $2.25

Step-by-step explanation:

5 lbs = 80 oz, so the mixture is worth

80(8/16) + 16(11) = 96x

x = $2.25/oz

Hope this helps!!

Answer:

[tex] \frac{6}{20} = \frac{3}{10?} [/tex]

Step-by-step explanation:

total amount of acts = 4+10+6 = 20

amount of dancers = 6

probability of picking a dancer = number of dancers / total number of talents = 6/20 = 3/10

The probability that a dancer performs first is 3/10.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers.

Total participants = 4+ 10 +6 = 20

So, the probability that a dancer performs first

= 6 /20

= 3/10

Hence, the probability that a dancer performs first is 3/10.

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The money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000

The formula for compound interest is given as;

[tex]A = P ( 1 + \frac{r}{n} )^n^t[/tex]

P = principal interest = $25, 000

r = rate = 4. 5%

n = 2 months

t = 6 years

A = [tex]25, 000 ( 1 + \frac{4. 5}{2} )^2 ^*^6[/tex]

A = [tex]25, 000(1 + 0. 75)^1^2[/tex]

A = [tex]25, 000( 825. 00)[/tex]

A = $20, 625, 000

Thus, the money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000

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Answer:

Question 6) Neither (Not an inverse variation)

Question 7) Inverse variation

Question 8) Inverse variation

Step-by-step explanation:

These are the two formulas we need to know prior to solving the question.

Direct variation: c times x

Inverse variation: c times 1/x --> c/x

- Here, c is the constant

6. y = x + 7

This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.

7. 14 = xy

This equation is an inverse variation.

xy = 14

y = 14/x

14 is the constant, and the format is the same as for an inverse variation.

8. x = -8/y

This equation is an inverse variation.

yx = -8

y = -8/x

-8 is the constant, and the format is the same as for an inverse variation.

So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.

General forms

Direct

Inverse

so

#6

Not inverse and direct also as 7 is present

#7

Yes

#8

Yes

The the next step in the proof is D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

It should be noted that vertical angles are the angles that are opposite each other when the two line cross.

In this case, 7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

In conclusion, the correct option is D.

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The question is an illustration of combination and there are 729 potential pass codes available

The given parameters are

Symbols available = 9

Length of pass code = 3

From the question, we understand that a symbol may be entered any number of times.

This means that each of the 9 available symbols can be used three times

So, the number of potential pass codes is

Passcodes = 9 * 9 * 9

Evaluate the product

Passcodes = 729

Hence, there are 729 potential pass codes available

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Answer:

Area of parallelogram = 9600 m²

Step-by-step explanation:

• We can find the measure of angle x using the cos rule:

[tex]160^2 = 100^2 +100^2 -2(100)(100) \cdot cos (x)[/tex]

Make x the subject of the equation:

⇒  [tex]20000 \cdot cos(x) = 100^2 +100^2 - 160^2[/tex]

⇒  [tex]cos(x) = -0.28[/tex]

⇒  [tex]x = cos^{-1} (-0.28)[/tex]

⇒  [tex]x = 106.26 \textdegree[/tex]

• Now we can find the area of one the triangles formed using the formula:

[tex]Area =\frac{1}{2} ab \cdot sin \theta[/tex]

where a and b are two sides of a triangle, and θ is the angle between them (angle x).

Substituting the values:

Area of one triangle = [tex]\frac{1}{2}[/tex]  × (100)(100) × sin(106.26°)

                             = 4800 m²

• Since the parallelogram is formed by two such triangles, we have to double the area of the triangle to find the parallelogram's area:

Area of parallelogram = 2 × 4800

                                     = 9600 m²

The management salary is $19,429

What is ratio?

Ratio is the quantitative relationship between two numbers which shows the number of times an amount or a number is contained within the other amount or number.

In this case, a ratio  of 8:7 shows the number of times the management salaries is contained within the management trainee salary

The management salary has a  value of 8 whereas the management trainee salary has a value of 7 as shown below:

salary ratio=management salary/management trainee salary

salary ratio=8/7

management salary=unknown(assume it is X)

management trainee salary=$17,000

8/7=X/$17,000

cross multiply

8*$17,000=7*X

X=8*$17,000/7

X=$19,429

The fact that annual management trainee salary is $17,000 means that the management salary is $19,429 annually.

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Answer:

standard deviation sign is σ

mean sign is x , and sometimes it have a hyphen directly above x.

Step-by-step explanation:

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list. To find the mean, add up all the values in the set. Then divide the sum by how many values there are.

The symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

Polynomials can be expressed as a product of binomials of the form (x - r) multiplied by a leading coefficient. The least polynomial contain the number of roots presented in statement, whose factor form is shown below:

f(x) = 1 · (x + 3)³ · x³ · (x - 3)

f(x) = (x + 3)³ · (x⁴ - 3 · x³)

f(x) = (x³ + 9 · x² + 27 · x + 27) · (x⁴ - 3 · x³)

f(x) = x⁷ + 9 · x⁶  + 27 · x⁵ + 27 · x⁴ - 3 · x⁶ - 27 · x⁵ - 81 · x⁴ - 81 · x³

f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

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It looks like the equation is

[tex]\dfrac{du}{dt} = 2t + \dfrac12 \sec^2(t) u[/tex]

with initial value [tex]u(0) = \frac\pi2[/tex].

Rearrange the equation to

[tex]\dfrac{du}{dt} - \dfrac12 \sec^2(t) u = 2t[/tex]

Multiply both sides by the integrating factor

[tex]\displaystyle \mu = \exp\left( \int -\frac12 \sec^2(t)\,dt\right) = \exp\left(-\frac12\tan(t)\right)[/tex]

and solve for [tex]u[/tex].

[tex]\implies e^{-\frac12 \tan(t)} \dfrac{du}{dt} - \dfrac12 \sec^2(t) e^{-\frac12 \tan(t)} u = 2t e^{-\frac12 \tan(t)}[/tex]

[tex]\implies \dfrac{d}{dt}\left[e^{-\frac12 \tan(t)} u\right] = 2t e^{-\frac12 \tan(t)}[/tex]

By the fundamental theorem of calculus, integrating both sides yields

[tex]e^{-\frac12\tan(t)} u = e^{-\frac12\tan(t)} u \bigg|_{t=0} + \displaystyle \int_{\xi=0}^{\xi=t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]

[tex]\implies e^{-\frac12\tan(t)} u = 1\times\dfrac\pi2 + \displaystyle \int_{0}^{t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]

[tex]\implies \boxed{\displaystyle u = \frac\pi2 e^{\frac12\tan(t)} + 2e^{\frac12\tan(t)} \int_0^t \xi e^{-\frac12 \tan(\xi)} \, d\xi}[/tex]