Jenna danced for 3 hours on Sunday, 2 hours on Monday and Tuesday, 1 hour on Thursday, 1.5 on Friday, and 2 hours on Saturday. She didn’t dance at all on Wednesday. What is the average number of hours she danced each day? Round your answer to the nearest tenth in an hour.

Answer:

AA

Step-by-step explanation:

See In Triangle ABC and Triangle STU

[tex]\because\begin{cases}\sf \angle A=\angle S=90° \\ \sf \angle B=\angle T=31°\end{cases}[/tex]

Hence

[tex]\sf \Delta ABC~\Delta STU(Angle-Angle)[/tex]

By AA similarity  triangle ABC is similar to triangle SUT. Therefore, option A is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

In the given triangle ABC, ∠C=180°-90°-31°

∠C=59°

In the given triangle SUT, ∠U=180°-90°-31°

∠U=59°

Here, ∠B=∠T (Given)

∠C=∠U (Obtained using angle sum property of a triangle)

So, by AA similarity ΔABC is similar to ΔSUT.

Therefore, option A is the correct answer.

To learn more about the similar triangles visit:

https://brainly.com/question/25882965.

#SPJ7

Answer:

[tex]x = y^3+5y[/tex]

Step-by-step explanation:

Complete question

[tex]\frac{x - 5y}{y^3} - 1=0\\[/tex]

Required

Solve for x

We have:

[tex]\frac{x - 5y}{y^3} - 1=0[/tex]

Collect like terms

[tex]\frac{x - 5y}{y^3} = 1[/tex]

Multiply through by [tex]y^3[/tex]

[tex]x - 5y = y^3[/tex]

Make x the subject

[tex]x = y^3+5y[/tex]

Answer:

f(g(1)) = - 2

Step-by-step explanation:

Find g(1) then use the value obtained to find f(x)

g(1) = 1 ← value of y when x = 1 (1, 1 ) , then

f(1) = - 2 ← value of y when x = 1 (1, - 2 )

Answer:

000023 because if we take three 0's we can get 000023 and 417 million

Answer:

Let the number of courses that are worth 3 credits each be x and those worth 4 credits be y. With the given information, you can write the following equations:  

x + y = 48

3x + 4y = 155

You can solve the above equations by method of elimination/substitution

x + y = 48 ⇒ x = 48 - y (Now, substitution this equation into 3x + 4y = 155)

3(48 - y) + 4y = 155

144 -3y + 4y = 155

y + 144 = 155

y = 11

Now plug this solution back into x = 48 - y  

x = 48 - 11 = 37  

Check work (by plugging the solutions back into the 3x + 4y and see if it's equal to 155):

3(37) + 4(11) = 155

Answer: There are 37 of the 3-credit course and 11 of the 4-credit course

Answer:

Just to recap, an equation has no solution when it results in an incorrect "equation".

For  example:

Equation: x+3 = x+4

Subtract x: 3 = 4???

But clearly, 3 is not equal to 4, so this equation has NO SOLUTION.

Now onto our problem:

13y+2-2y = 10y+3-y

11y+2 = 9y+3

2y=1

y=1/2

9(3y+7)-2 = 3(-9y+9)

27y+61 = -27y+27

54y = -34

y = -34/54

32.1y+3.1+2.4y-8.2=34.5y-5.1

34.5-5.1=34.5y-5.1

5.1=5.1

infinite solutions

5(2.2y+3.4) = 5(y-2)+6y

11y+17 = 11y-10

17 = -10??

That's not true, so the option "5(2.2y+3.4) = 5(y-2)+6y" has no solution.

Let me know if this helps

Answer:

The AP is 1, 11/2, 10, 29/2, 19, ....

Step-by-step explanation:

Let the first term be a and d be the common difference of the arithmetic progression.

ATQ, a+2d+a+6d=38, 2a+8d=38 and a+8d=37. Solving this, we will get a=1 and d=9/2. The AP is 1, 11/2, 10, 29/2, 19, ....

Answer:

$465.6 should be budgeted.

Step-by-step explanation:

Normal Probability Distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean $440 and standard deviation $20.

This means that [tex]\mu = 440, \sigma = 20[/tex]

How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1?

The 100 - 10 = 90th percentile should be budgeted, which is X when Z has a p-value of 0.9, so X when Z = 1.28. Then

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

[tex]1.28 = \frac{X - 440}{20}[/tex]

[tex]X - 440 = 1.28*20[/tex]

[tex]X = 465.6[/tex]

$465.6 should be budgeted.

Answer:

c.145.3 to 154.7.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{20}{\sqrt{50}} = 4.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 4.7 = 145.3.

The upper end of the interval is the sample mean added to M. So it is 150 + 4.7 = 154.7.

Thus the correct answer is given by option c.

Answer:

h = 6[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The given is the special right triangle with angle measures : 90-60-30

and the side lengths for the given angles are represented by :

2a-a[tex]\sqrt{3}[/tex]-a

the side length that sees 60 degrees is represented by a[tex]\sqrt{3}[/tex] (h in this case)

the area of a triangle is calculated by multiplying height and base and that is divided by 2

a[tex]\sqrt{3}[/tex]*a/2 = 18[tex]\sqrt{3}[/tex] multiply both sides by 2

a^2[tex]\sqrt{3}[/tex] = 36[tex]\sqrt{3}[/tex] divide both sides by [tex]\sqrt{3}[/tex]

a^2 = 36 find the roots for both sides

a = 6

since h sees angle measure 60 and is represented by a[tex]\sqrt{3}[/tex]

h = 6[tex]\sqrt{3}[/tex]

Answer:

The right answer is:

(a) 0.1456

(b) 18.125, 69.1202, 8.3139

Step-by-step explanation:

Given:

N = 24

n = 5

r = 7

The improperly drilled gearboxes "X".

then,

⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]

(a)

P (all gearboxes fit properly) = [tex]P(x=0)[/tex]

                                               = [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]

                                               = [tex]0.1456[/tex]

(b)

According to the question,

[tex]X = 91+5[/tex]

Mean will be:

⇒ [tex]\mu = E(x)[/tex]

       [tex]=E(91+5)[/tex]

       [tex]=9E(1)+5[/tex]

       [tex]=9.\frac{nr}{N}+5[/tex]

       [tex]=9.\frac{5.7}{24} +5[/tex]

       [tex]=18.125[/tex]

Variance will be:

⇒ [tex]\sigma^2=Var(X)[/tex]

         [tex]=V(9Y+5)[/tex]

         [tex]=81.V(Y)[/tex]

         [tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]

         [tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]

         [tex]=69.1202[/tex]

Standard deviation will be:

⇒ [tex]\sigma = \sqrt{69.1202}[/tex]

       [tex]=8.3139[/tex]      

Answer:

Area of the metal sheet required = 364 square inches

Step-by-step explanation:

Area of the metal sheet required = Surface area of the lateral sides of the vent transition

Since, lateral sides of the vent is in the shape of a trapezoid,

Therefore, surface area of the vent = 4(Surface area of one lateral side)

                                                           = [tex]4[\frac{1}{2}(b_1+b_2)h][/tex]

Here, [tex]b_1[/tex] and [tex]b_2[/tex] are two parallel sides and [tex]h[/tex] is the distance between these parallel sides.

Surface area of the vent = [tex]4[\frac{1}{2}(8+5)14][/tex]

                                         = 364 square inches

Therefore, area of the metal sheet required = 364 square inches

[tex]\\ \sf\longmapsto (f+g)(x)[/tex]

[tex]\\ \sf\longmapsto f(x)+g(x)[/tex]

[tex]\\ \sf\longmapsto 4x-3+9x+2[/tex]

[tex]\\ \sf\longmapsto 4x+9x-3+2[/tex]

[tex]\\ \sf\longmapsto 13x-1[/tex]

Answer:

13x - 1

Step-by-step explanation:

f(x) + g(x) = 4x - 3 + 9x + 2

f(x) + g(x) = 4x+9x + 2 - 3

f(x) + g(x) = 13x - 1

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Answer:

  g, h, f

Step-by-step explanation:

A graph of two exponential curves will have the one with the least growth rate crossing under the one with the greater growth rate. Here, f(x) is shown crossing under g(x) and is on its way to a point of intersection with h(x). So, f(x) has the least growth rate.

g(x) and h(x) start out at about the same level, but g(x) curves upward faster, indicating it has the higher growth rate.

In order from greatest to least growth rate, the functions are ...

  g(x), h(x), f(x)

Answer:

a) 10,025 m = 10km 25m = 10.025 km

b) 1,500 m = 1 km 500 m = 1.5 km

Answer:

a) 10025m = 10km 25m = 10.025km

b) 1500m = 1km 500m = 1.5km

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit conversion.

Unit conversion is the conversion between different units of measurement for the same quantity.

1 km = 1000 m

Solve:

a)

b)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]

In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.

The number of times that each prime divides the original integer becomes its exponent in the final result.

In here,  Prime number 2 to the power of 2 equals 4.

[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]

First, We need to add fractions-

Rule:-

[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]

LCD = [tex]7 \cdot 2^{2}[/tex]

[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]

[tex]x=2[/tex]

OAmalOHopeO

the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.

The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.

In terms of hyperbola, F1F2=2c, c=20.

The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.

Use formula c^2=a^2+b^2c

2

=a

2

+b

2

to find b:

\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}

(20)

2

=(18)

2

+b

2

,

b

2

=400−324=76

.

The branches of hyperbola go in y-direction, so the equation of hyperbola is

\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1

b

2

y

2

−

a

2

x

2

=1 .

Substitute a and b:

\dfrac{y^2}{76}- \dfrac{x^2}{324}=1

76

y

2

−

324

x

2

=1 .

Answer:

Check the image

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Answer:

  C. EGD

Step-by-step explanation:

A major arc is typically named using the end points and a point on the arc. Here, the end points are E and D, and points on the major arc include C, G, and F. The major arc ED could be named any of

Of course, the reverse of any of these names could also be used: DCE, DGE, DFE.

Answer:

51 cents for 17 inches of wire

Step-by-step explanation:

22 = 66

17 = x

22x = 66 * 17

22x = 1122

x = 51 cents

or

22 inches costs 66 cents

1 inch costs 3  cents (66 / 22 = 3  cents)

17 inches costs 51  cents (17 * 3 = 51 cents)

Answer: 205.3

I suppose all measures of angles are done from the same axis (for example x-axis)

Step-by-step explanation:

You just have to use the theorem of Al'Kashi:

[tex]d^2=400^2+300^2-2*300*400*cos(30^o)\\\\d\approx{205.3(km)}[/tex]

Answer: 3

happy learning

Answer:

B.

Step-by-step explanation:

From the point (-1,0) the next point on the graph is up 3, right 1, making the slope a positive 3.

Answer:

Probability-Between    .8574 = 85.74%

Step-by-step explanation:

Z1=-2.14 Z2=1.14

*x-1 35

*x-2  58

*µ 50

*σ 7

Answer:

team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.

Step-by-step explanation:

Water drunk by Bobby in 10 hours = 5 units

So, water drink by Bobby in 1 hour

= 5/10 units

= 1/2 units

= 0.5 units

Answer:

1/2 water

Step-by-step explanation:

We can use a ratio to solve

5 waters        x waters

-----------   = ------------

10 hours             1 hours

Using cross products

5*1 = 10 *x

5 = 10x

Divide by 10

5/10 = x

1/2 waters =x

Answer:

2^(1/6) (cos(-pi/12)+i sin(-pi/12))

2^(1/6) (cos(3pi/12)+i sin(3pi/12))

2^(1/6) (cos(7pi/12)+i sin(7pi/12))

2^(1/6) (cos(11pi/12)+i sin(11pi/12))

2^(1/6) (cos(5pi/4)+i sin(5pi/4))

2^(1/6) (cos(19pi/12)+i sin(19pi/12))

Step-by-step explanation:

Let's convert to polar form.

-2i=2(cos(A)+i sin(A) )

There is no real part so cos(A) has to be zero and since we want -2 and we already have 2 then we need sin(A)=-1 so let's choose A=-pi/2.

So z=2(cos(-pi/2)+i sin(-pi/2)).

There are actually infinitely many ways we can write this polar form which we will need.

z=2(cos(-pi/2+2pi k)+i sin(-pi/2+2pi k))

where k is an integer

Now let's find the 6 6th roots or z.

2^(1/6) (cos(-pi/12+2pi k/6)+i sin(-pi/12+2pi k/6))

Reducing

2^(1/6) (cos(-pi/12+pi k/3)+i sin(-pi/12+pi k/3))

Plug in k=0,1,2,3,4,5 to find the 6 6th roots.

k=0:

2^(1/6) (cos(-pi/12+pi (0)/3)+i sin(-pi/12+pi (0)/3))

=2^(1/6) (cos(-pi/12)+i sin(-pi/12))

k=1:

2^(1/6) (cos(-pi/12+pi/3)+i sin(-pi/12+pi/3))

2^(1/6) (cos(3pi/12)+i sin(3pi/12))

k=2:

2^(1/6) (cos(-pi/12+2pi/3)+i sin(-pi/12+2pi/3))

2^(1/6) (cos(7pi/12)+i sin(7pi/12))

k=3:

2^(1/6) (cos(-pi/12+3pi/3)+i sin(-pi/12+3pi/3))

2^(1/6) (cos(11pi/12)+i sin(11pi/12))

k=4:

2^(1/6) (cos(-pi/12+4pi/3)+i sin(-pi/12+4pi/3))

2^(1/6) (cos(15pi/12)+i sin(15pi/12))

2^(1/6) (cos(5pi/4)+i sin(5pi/4))

k=5:

2^(1/6) (cos(-pi/12+5pi/3)+i sin(-pi/12+5pi/3))

2^(1/6) (cos(19pi/12)+i sin(19pi/12))

Answer:

The student is completely incorrect because there is no solution to this inequality.

Answer:

D on edge

Step-by-step explanation:

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Answer:

  7.92 years

Step-by-step explanation:

We want to find t such that ...

  3 = 2^(t/5)

where 2^(t/5) is the annual multiplier when doubling time is 5 years.

Taking logs, we have ...

  log(3) = (t/5)log(2)

  t = 5·log(3)/log(2) ≈ 7.92 . . . years

It will take about 7.92 years for the population to triple.

Answer:

y > -1

Step-by-step explanation:

the line is going across the y axis and is everything above -1