The figure shown consists of a rectangle and quarter circle ?

Answer:

[tex]AB= 20.9[/tex]

[tex]A = 33.2^\circ[/tex]

[tex]C = 54.8^\circ[/tex]

Step-by-step explanation:

Given

The above triangle

Required

Complete the lengths

To do this, we make use of sine rule.

[tex]\frac{a}{\sin A} = \frac{b}{\sin B}[/tex]

[tex]\frac{14}{\sin A} = \frac{24}{\sin 70}[/tex]

[tex]\frac{14}{\sin A} = 25.54[/tex]

Cross multiply

[tex]\sin A * 25.54 = 14[/tex]

[tex]\sin A = \frac{14}{25.54}[/tex]

[tex]\sin A = 0.5482[/tex]

Take Arc sine of both sides

[tex]A = sin^{-1}(0.5482)[/tex]

[tex]A = 33.2^\circ[/tex]

To calculate C, we have:

[tex]C = 180 -A-B[/tex] --- angles in a triangle

[tex]C = 180 -55.2-70[/tex]

[tex]C = 54.8^\circ[/tex]

Calculate length AB using the sine rule.

[tex]\frac{AB}{sin C} = \frac{AC}{B}[/tex]

So, we have:

[tex]\frac{AB}{sin 54.8} = \frac{24}{sin 70}[/tex]

Make AB the subject

[tex]AB= sin 54.8*\frac{24}{sin 70}[/tex]

[tex]AB= sin 54.8* 25.54[/tex]

[tex]AB= 20.9[/tex] -- approximated

Answer:

The athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.

Step-by-step explanation:

Given that at first an athlete jogs at 4 miles per hour and then jogs at 6 miles per hour, traveling 8 miles in 1.5 hours, to determine how long does the athlete jogs at each speed the following calculation must be performed:

4 x 1.5 + 6 x 0 = 6

4 x 1 + 6 x 0.5 = 7

4 x 0.75 + 6 x 0.75 = 7.5

4 x 0.5 + 6 x 1 = 8

Therefore, the athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.

Answer:

Step-by-step explanation:

( x + 3) (2x - 7)

x(2x - 7) + 3(2x - 7)

Answer:

x = -2

Step-by-step explanation:

4(x + 5) = 12

4x + 20 = 12

4x + 20 - 20 = 12 - 20

4x = -8

4x / 4 = -8 / 4

x = -2

Hope this helps, thank you :) !!

Answer:

880x+30

880    880

x=29.3 repeating

Step-by-step explanation: Hope this helps

Answer:

9,942 bacteria were there at 10 hours.

Step-by-step explanation:

Equation for population decay:

The equation for population decay, after t hours, is given by:

[tex]P(t) = P(0)(1-r)^t[/tex]

In which P(0) is the initial population and r is the decay rate, as a decimal.

Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours.

This means that [tex]P(0) = 200000[/tex] and that when [tex]t = 18, P(t) = 900[/tex]. So we use this to find r.

[tex]P(t) = P(0)(1-r)^t[/tex]

[tex]900 = 200000(1-r)^{18}[/tex]

[tex](1-r)^{18} = \frac{900}{200000}[/tex]

[tex]\sqrt[18]{(1-r)^{18}} = \sqrt[18]{\frac{900}{200000}}[/tex]

[tex]1 - r = (\frac{900}{200000})^{\frac{1}{18}}[/tex]

[tex]1 - r = 0.7407[/tex]

So

[tex]P(t) = P(0)(1-r)^t[/tex]

[tex]P(t) = 200000(0.7407)^t[/tex]

At this rate of decay, how many bacteria was there at 10 hours?

This is P(10). So

[tex]P(10) = 200000(0.7407)^{10} = 9941.5[/tex]

Rounding to the nearest whole number:

9,942 bacteria were there at 10 hours.

[(2x³y⁴)² × 2x]½

(2x³y⁴)½ ×(2x)½

2x³y⁴(2x)½

Answer:

(whats 1girl + 1 girl=) uhh ima go with 2girl ;)

Step-by-step explanation:

whats 1girl + 1 girl=?

well 1+1=2 so 1girl + 1 girl= 2girl

Answer: I love these... Okay so the exterior angle is equal to the two remote interior angles meaning that 120 would be equal to 15x+5+22x+4 which is 70

Step-by-step explanation:

Answer:

x= 12

Step-by-step explanation:

11x+2=134

-2 -2

_________

11x = 132

__ ___

11 11

x=12

9514 1404 393

Answer:

  C. ... 3 1/4 cups

Step-by-step explanation:

The problem statement tells you that the other measures are combined. That means you're looking for an expression like ...

  3/8 × ((3 2/3) +(2 1/4) +(2 3/4))

This eliminates choices B and D.

If you look at the numbers in parentheses, you see that the 1/4 and 3/4 will have a sum of 1, so the only fraction in the sum will be 2/3. This eliminates choice A.

The only viable answer choice is C.

__

If you like, you can check to see that answer C is correct.

  (3/8)(8 2/3) = (3/8)(26/3) = 26/8 = 3 2/8 = 3 1/4

Answer:

i^12

Step-by-step explanation:

there is no further answer

Answer:

i^12 = 1  

One to any power is one.?

Answer:

the radius is 4 inches

Step-by-step explanation:

diameter/2=radius

Answer: 4 inches

Step-by-step explanation: r= d/2=/2=4inches

Person above is wrong, the answer is D on Edge.

D. y1 = log x/log 6, y2 = log (x + 4)/log 2

Answer:

its D on edge 2021

Step-by-step explanation:

i took the test

Answer:

Question 1: Statistical

Question 2: Not Statistical

Step-by-step explanation:

Given

Question 1 and 2

Required

Are they statistical questions?

A question is said to be statistical if it can be answered through data collection and if there are variances in the collected data.

Using this yardstick, we can say that (1) is a statistical question because the frequency at which the band perform in a week can be determined by gathering data of their past practice.

This can not be said of (2) because (2) has not been done yet, there is no available data to make predictions and lastly, the variance of an unavailable data can not be determined.

Answer:

the ratio of food costs to take home dollars is 1:6

Step-by-step explanation:

The computation of the ratio of the foods cost to take home is shown below:

Given that

Monthly take home pay is $1,500

And, the spending month on food is $250

Based on the  above information

The ratio is

= $250 ÷ $1500

= 1:6

Hence, the ratio of food costs to take home dollars is 1:6

Answer:

it would be -11x^2+11x-4

Answer:

part A) yes, the bases and heights are the same

Part B) yes, the bases and heights are the same

Part C) not enough info

Step-by-step explanation:

Part C)

area of the circle = π(1/2h)²

area of ellipse = π(1/2h)(1/2 major axis)

Answer:

we cant see the problem

Step-by-step explanation:

Answer:

cash price:

10% = 250

2500 - 250 = $2,250

hire purchase:

2500 + 500 + 150(18) = $5,700

a) 5,700 - 2,250 = $3,450

Answers:

6 pints = 12 cups

16 pints = 8 quarts

8 fluid ounces = 1 cup

8 pints = 1 gallon

Answer:

C. 26 + 4x = 46

Answer:

C

Step-by-step explanation:

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that 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 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

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.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that [tex]\sigma = 2[/tex]

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when [tex]M = 0.5[/tex]. So

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

[tex]0.5 = 1.96\frac{2}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 2*1.96[/tex]

Dividing both sides by 0.5

[tex]\sqrt{n} = 4*1.96[/tex]

[tex](\sqrt{n})^2 = (4*1.96)^2[/tex]

[tex]n = 61.5[/tex]

Rounding up

We would have to take a sample of 62 to achieve this result.

9514 1404 393

Answer:

  (a)  7

Step-by-step explanation:

The congruence statement tells you that AC ≅ AE. AC is marked as 7, so ...

  AE = 7

_____

Additional comment

If you solve the triangle using the Law of Sines, you find that AC = AE = 6.484, not 7.

Answer:

A

Step-by-step explanation: