the measures of three angles of a triangle are given by (8x-10), (2x), and (3x-5). What is the measure of the larges tangle

Answer: C

<BFE is 148 degrees

Step-by-step explanation:

We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?

1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same

2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.

3. Now, we have all the angles we need to find out <BFE.

4. <BFC+<CFD+<DFE=<BFE

5. Substitute to get

57+34+57=<BFE

91+57=<BFE

148=<BFE

6. Now we know that the answer is 148 degrees.

Answer:

Step-by-step explanation:

The focus lies above the vertex, so the parabola opens upwards.

Answer:

It cannot be 0

Step-by-step explanation:

it can also be positive number :2/4

it can be odd number too:3/9

it is bigger than numerator bcoz we have to divide it for numerator

So, 0 number cannot be put as denominator in fraction is true statement

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

Answer:

The slope is undefined.

Step-by-step explanation:

The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 were dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

9514 1404 393

Answer:

  y = -9x +49

Step-by-step explanation:

The slope of line b is the same as the slope of line a. That can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -8)/(2 -1) = -9

The y-intercept can be found from the given point using the formula ...

  b = y - mx

  b = 13 -(-9)(4) = 13 +36 = 49

Then the slope-intercept equation of line b is ...

  y = -9x +49

If y (0) = -1/3, then

-1/3 = 1 / (1 + C e ⁻⁰)

Solve for C :

-1/3 = 1 / (1 + C )

-3 = 1 + C

C = -4

So the particular solution to the DE that satisfies the given initial condition is

[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]

9514 1404 393

Answer:

  6 units

Step-by-step explanation:

The dilation factor is 2, so the length of A'B' will be 2 times the length of AB.

AB can be seen to be 3 units, so A'B' will be 2×3 = 6 units.

Answer:

f(-1) = 2-3(-1) +1

= 7

f(-3)= 2-3(-3)+1

= 12

f(-1) = -1-1

= -2

f(-3) = -3-1

= -4

Answer:

The point is a solution

Step-by-step explanation:

y = x^2

Substitute the point into the equation and see if it is true

0 = 0^2

0=0

True

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Answer:

  (b)  0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

  (4x +15y) -6(2/3x +5/2y) = (12) -6(15)

  0 = -78

Answer:

the answer is b

Step-by-step explanation:

Answer:

Always. Always.

Step-by-step explanation:

All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.

Answer:

135

Step-by-step explanation:

Given that :

Total score obtained by Peter, Jan and Maxim = 269

Let :

Peter's score = x

Jan's score = y

Maxim's score = z

x + y + z = 269

x > (y + z)

For x to be greater Than y + z ;

Then x > (269 / 2) ; x > 134.5

The least possible x score is 135

Hence, Peter's least possible score is 135.

Answer:

12

Step-by-step explanation:

Scale factor of 4

CD = 3

3 · 4 = 12

Length of C'D' is 12 units

Answer:

12 units

Step-by-step explanation:

The original segment CD = 3 units

Scale factor is 4.

3 x 4 = 12

Answer:

Option C

Step-by-step explanation:

thankful that there are graphing tools. see screenshot

Answer:

(-2,2) and (-3,-4)

Step-by-step explanation:

by graphing the line and parabola, you should get this graph

Answer:

Step-by-step explanation:

cotθ = cosθ/sinθ = 2/3

sinθ = 3/√(2²+3²) = 3/√13

cscθ = 1/sinθ = √13/3

Answer:

8 minuets

Step-by-step explanation:

24min/3miles = 8

Answer:

8 minutes.

Step-by-step explanation:

If we divide 24 minutes by 3 miles, your answer will be 8 minutes.

Answer:

[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]

The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,

[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]

Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.

So you have

• upper estimate:

(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)

= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)

= 70.2 L

• lower estimate:

(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)

= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)

= 63.2 L

Answer:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x

15,068 mi/hr

Step-by-step explanation:

[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]

[tex]=15,068\:\text{mi/hr}[/tex]

The speed of 22100 feet per second will be 15068.18 miles per hour.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.

Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,

22100 ft /s = ( 22100 x 3600 ) / 5280

22100 ft/s = 79560000 / 5280

22100 ft/s = 15068.18 miles per hour

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Answer:

a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.

This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]

The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

Question b:

30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

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Answer:

  arithmetic; common difference of 5

Step-by-step explanation:

It usually works well to check differences first. Here, they are ...

  8 -3 = 5

  13 -8 = 5

These are the same value, so the sequence is arithmetic with a common difference of 5.

Answer:

0.3736

Step-by-step explanation:

46.7 percent of  [tex]\frac{4}{5}[/tex] is 0.3736.

To find 46.7% of [tex]\frac{4}{5}[/tex].

So,

[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]

[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]

⇒ [tex]0.3736[/tex]

Therefore,  46.7% of  [tex]\frac{4}{5}[/tex] is 0.3736.

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Answer:

180000 people

1 : 2

$40

80 stores

Step-by-step explanation:

1.)

Population in 2020 are equal : Let population =

City A increased by 20% From 120,000 in 2015

(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000

Hence, city A = 144,000.

Since, city A and B have equal population ; city B also has a population of 144000 in 2020.

Let population in 2015 = x

(1 - 0.2) * x = 144000

0.8x = 144000

x = 144000/0.8

x = 180,000

2.)

Let proportion of 20% butter = x and proportion of 50% butter = 1 - x

0.2x + 0.5(1 - x) = 0.4

0.2x + 0.5 - 0.5x = 0.4

-0.3x + 0.5 = 0.4

-0.3x = 0.4 - 0.5

-0.3x = - 0.1

x = 0.1/0.3

x = 0.3333

(1-x) = 1 - 0.33333 = 0.6666%

0.3333% of 20% butter

0.6666% of 50% butter

Hence ;

0.3333 : 0.6666

1 : 2

3.)

Let original price of book = x

Discount on sale = 30%

Sale price = $28

Sale price = original price * (1 - discount)

$28 = (1 - 0.3) * x

$28 = 0.7x

x = $28/0.7

x = $40

4.)

Let total number of stores = x

Store surveys needed = 32

40% of total stores = 32 stores

0.4x = 32

x = 32 / 0.4

x = 80