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Question 1
Solve the equation for X.
4(3x + 2) = 68

Answer:

[tex]\sf x= 14.04^{\circ \:}[/tex]

using tan rule:

[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

solve:

[tex]\rightarrow \sf tan(x)= \dfrac{5}{20}[/tex]

[tex]\rightarrow \sf x= tan^{-1}(\dfrac{5}{20})[/tex]

[tex]\rightarrow \sf x= 14.04^{\circ \:}[/tex]

Answer:

x = 14.04° (nearest hundredth)

Step-by-step explanation:

Use the tan trig ratio:

[tex]\mathsf{\tan(\theta)=\dfrac{O}{A}}[/tex]

where:

Given:

[tex]\implies \mathsf{\tan(x)=\dfrac{5}{20}}[/tex]

[tex]\implies \mathsf{x=\arctan\left(\dfrac{5}{20}\right)}[/tex]

[tex]\implies \mathsf{x=14.04\textdegree \ (nearest \ hundredth)}[/tex]

Answer:

[tex]y = \frac{x}{2} + 4[/tex]

Answer:

77

Step-by-step explanation:

<DBE and <ABE are supplementary angles so their sum is equal to 180

<DBE is given as 103

103 + <ABE = 180 subtract 103 from both sides

<ABE = 77

Answer:

what is the answer i dont know you tell him to ask another person because i m back bencheer

Answer:

2/5x6/7 = 12/35

Step-by-step explanation:

when we multiply fractions we multiply the denominators together and the numerators as well, so 2 x 6 = 12. and  5 x 7 =35

12/35

Answer:

£0.60

Step-by-step explanation:

If each pack costs £1.59 and Nadia orders 15 packs,

then the total order before discount = 1.59 x 15 = £23.85

From the table given, we can see that for an order of £23.85 a 2.5% discount will be applied.

Divide £23.85 by 100 to get 1%:  £23.85 ÷ 100 = £0.2385

Now multiply by 2.5 to get 2.5%:  £0.2385 × 2.5 = £0.59625 = £0.60

Alternatively, the calculation in one expression is:

(1.59 × 15) × 0.025 = 0.59625

Answer:

-x^2 +10x + 7

[tex]-x^2 +10x + 7[/tex]

Step-by-step explanation:

its the gray shaded area [(x+1)*(x+7)] minus the white area [(x-1)*(2x)]

AKA: [(x+1)*(x+7)] - [(x-1)*(2x)]

so first you foil to get both areas

gray region: (x+1)*(x+7) = x^2 + 8x + 7

white region: (x-1)*(2x) = 2x^2 - 2x

and then you subtract the white from the gray

[tex](x^2 + 8x + 7) - (2x^2 - 2x)[/tex]

-x^2 +10x + 7

Answer:

<aob=1/2(can + ab)

<aob=1/2(25+46)

<aob=1/2(71)

<aob=35.5

Answer:

y = 90[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then using the 45° angle on the lower left

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{90}{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

y = 90[tex]\sqrt{2}[/tex]

Answer:

[tex]\frac{5}{8}[/tex]  

I hope this helps!

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

to multiply fractions, multiply the numerators together then the denominators.

5 * 3 = 15

6 * 4 = 24

15/24

now simplify that fraction.

15/24

divide both sides by 3

5/8

Answer: 72 square feet

Step-by-step explanation: just multiply 8* 7 = 56 then 8*2 = 16 and add = 72

Answer:

cable 1 ≈ 54.63 ft

Step-by-step explanation:

using Pythagoras' identity in the right triangle having cable 1 as its hypotenuse.

let cable 1 be x , then

x² = 22² + 50² = 484 + 2500 = 2984 ( take square root of both sides )

x = [tex]\sqrt{2984}[/tex] ≈ 54.63 ft ( to 2 dec. places )

Answer:

area= base(length)*height(width)

possible dimensions

4 *3, 3*4

6*2, 2*6

12*1, 1*12

Answer:

meter (m) is the standard unit measurement for length .

Answer:

it is meter just to let yall know

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given data

total distance=160 cm

time taken =20seconds

We know that speed =distance/time

So let us solve for the speed of the ant

speed=160/20

speed= 8cm/s

Also when the distance is 216,and the ant uses the same speed,it will take the ant

time=distance/speed

time=216/8

time= 27seconds

Answer:

is called a controlled operation

Step-by-step explanation:

that's what its called i just know

Based on the estimate from the Waldfogel study, 10[tex]\%[/tex] of this would be a deadweight loss, i.e., [tex]\[/tex]90.6 would be the deadweight loss.

Deadweight loss means the economic inefficiency that takes place when the allotment of resources in a market isn't at the optimal position.

The study suggested that the average recipient's valuation of the gift received was approximately 90[tex]\%[/tex] of the actual purchase price of the gift.

This means that 10[tex]\%[/tex] of the value of the gift gets lost in between.

This loss of 10[tex]\%[/tex] in value constitutes the deadweight loss.

The average amount spent on gifts = $906

Percentage loss in value = 10[tex]\%[/tex] or 0.10

Calculation of the deadweight loss,

DWL = Average amount spent on gifts × Percentage loss in value

DWL = [tex]\[/tex]906 × 0.10

Thus, the deadweight loss would be [tex]\[/tex]90.6.

Learn more about a deadweight loss here:

https://brainly.com/question/32082652

#SPJ12

Answer:

-1/4x+3/4

or

-0.25x+0.75

Step-by-step explanation:

g(x) = mx + b

m = slope

b = initial value

m = -1/4

b = 3/4

g(x) = -1/4x+3/4

Hope this helped, let me know if you need more help!

Answer:

28.26

Step-by-step explanation:

[tex]3.14\times9[/tex]

Calculate the product or quotient
[tex]28.26[/tex]

I hope this helps you

:)

Answer:

i think its a

Step-by-step explanation:

Recall the double angle identity,

sin(2x) = 2 sin(x) cos(x)

Then we can write

sin(9x) cos(9x) = 1/2 sin(2 • 9x) = 1/2 sin(18x)

Then

∫ sin(9x) cos(9x) dx

= 1/2 ∫ sin(18x) dx

= -1/2 • 1/18 cos(18x) + C

= -1/36 cos(18x) + C

though you could continue with another double angle identity,

cos(2x) = cos²(x) - sin²(x)

to rewrite the antiderivative as

= -1/36 (cos²(9x) - sin²(9x)) + C

= 1/36 (sin²(9x) - cos²(9x)) + C

Answer:

The juice bar can sell 3 more cups of the passion juice than the berry juice (last one)

Step-by-step explanation:

Passion: 768/16=48

Berry: 810/18=45

passion can fill 48 cups while berry can fill 45 cups, so passion fills +3

:)

Complete options are;

a. The approximation requires np > 10 and n(1 - p) > 10.

b. The sample size here is too small to use the Normal approximation to the binomial.

c. The approximation requires np > 30.

d. The Normal approximation works better if the success probability p is close to p = 0.5.

Answer:

Option C is false

Step-by-step explanation:

Looking at the options,

In normal approximation to the binomial,

n is the sample size,

p is the given probability.

q = 1 - p

Now, one of the conditions for using normal approximation to the binomial is that; np and nq or n(1 - p) must be greater than 10.

This means that option A is true because we require np or n(1 - p) to be greater than 10.

From Central limit theorem, the sample size needs to be more than 30 for us to use normal approximation. Our sample is 10. Thus, option B is true.

The approximation doesn't require np > 30. Rather it's the sample size that needs to be more than 30. Thus, option C is false.

Generally, when the value of p in a binomial is close to 0.5, the normal approximations will work better than when the value of p is closer to either 0 or 1. The reason is that: for p = 0.5, the binomial distribution will be symmetrical. Thus, option D is correct.

Answer:

he first one worked 15 hours, the second one worked 5 hours.

Step-by-step explanation:

First mechanic worked x hours, then second one worked 20 - x hours

First one charged $95*x, second one charged $75*(20-x)

Total charge = 95x + 75(20 - x) = 1800

95x + 1500 - 75x = 1800

20x = 300

x = 15, 20 - x = 5

So the first one worked 15 hours, the second one worked 5 hours.

Answer:

1

Step-by-step explanation:

Anything to the exponent of 0 is 1.