Question 3 of 10
Which angle in ABC has the largest measure?
2
С
A ZA
B. 8
C. 20
O O
D. Cannot be determined

Answer:

C. 12, 8, 5

Step-by-step explanation:Side lengths of any triangle must conform to the triangle inequality theorem, which says that the sum of the lengths of any of the two sides of the triangle is greater than the length of the third side.

This means:

a + b > c

a + c > b

b + c > a

Let's check each of the options to see which set are possible lengths for a triangle:

A. 6, 5, 11

6 + 11 > 5 ===> 17 > 5

5 + 11 > 6 ===> 16 > 6

6 + 5 > 11 ===> 11 > 11 (INCORRECT. Does not confirm to tye theorem)

Therefore, this set cannot be possible side lengths for a triangle.

B. 8, 1, 2

8 + 1 > 2 ===> 9 > 2

1 + 2 > 8 ===> 3 > 8 (INCORRECT)

8 + 2 > 1 ===> 10 > 1

This set cannot be possible side lengths for a triangle.

C. 12, 8, 5

12 + 8 > 5 ===> 20 > 5

8 + 5 > 12 ===> 13 > 12

12 + 5 > 8 ===> 17 > 8

All are correct, therefore these are possible side lengths for a triangle.

Answer:

1/3

Step-by-step explanation:

common ratio is

9÷27=1/3

3÷9=1/3

1÷3=1/3

therefore common ratio is 1/3

Answer: 1/3

Step-by-step explanation:

Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.

Answer:

2.3

Step-by-step explanation:

.5 - .3 = .2

.8 - .5 = .3

1.2 - .8 = .4

1.7 - 1.2 = .5

We should add .6 next

1.7+.6 = 2.3

Answer:

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Step-by-step explanation:

Before building the confidence intervals, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

In the morning:

Sample of 57, mean of 5.2, standard deviation of 0.6, so:

[tex]\mu_1 = 5.2[/tex]

[tex]s_1 = \frac{0.6}{\sqrt{57}} = 0.0795[/tex]

In the afternoon/evening:

Sample of 70, mean of 4.5, standard deviation of 0.4, so:

[tex]\mu_2 = 4.5[/tex]

[tex]s_2 = \frac{0.2}{\sqrt{70}} = 0.0239[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 5.2 - 4.5 = 0.7[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0795^2 + 0.0239^2} = 0.083[/tex]

Confidence interval:

The confidence interval is:

[tex]\mu \pm zs[/tex]

In which

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

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower bound of the interval is:

[tex]\mu - zs = 0.7 - 1.96*0.083 = 0.5[/tex]

The upper bound of the interval is:

[tex]\mu + zs = 0.7 + 1.96*0.083 = 0.9[/tex]

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Answer:

17ft

Step-by-step explanation:

5*2 + 3.5*2=17

Answer:

y=12x+10

Step-by-step explanation:

Slope-intercept form is y=mx+b

1. Add -12x to both sides of the equation

Answer:

No, because the ratio of pay to hours is not the same for each pair of value.

Answer:

Step-by-step explanation:

3

Answer:

2x + 30° = 40°

4x + 30° = 50°

Step-by-step explanation:

2x + 30° and 4x + 30° are complementary angles.

Complementary angles sum up to give 90°.

Therefore,

2x + 30° + 4x + 30° = 90°

Add like terms

6x + 60 = 90

6x = 90 - 60

6x = 30

6x/6 = 30/6

x = 5

✔️2x + 30°

Plug in the value of x

2(5) + 30

10 + 30

= 40°

✔️4x + 30°

4(5) + 30°

20 + 30

= 50°

Answer:

Step-by-step explanation:

Answer:

622,080

Step-by-step explanation:

The total number of subjects is 3

= 3×2×1

= 6

Six maths book

= 6×5×4×3×2×1

= 720

Four physics book

= 4×3×2×1

= 24

Three chemistry book

= 3×2×1

= 6

6×720×24×6

= 622,080

Hence if the books are grouped together 622,080 arrangement is possible

d. 12ft

Answer:

Solution given:

∆ABC is similar to∆MBN

since their corresponding side are proportional.

so

AB/MB=AC/MN

[since AM=BM=4ft

AB=AM+BM=4+4=8ft]

8/4=AC/6

doing crisscrossed multiplication

2*6=AC

AC=12ft

Answer:

(x-2)^2 +(y+3)^2 >36 and (x-4)^2 +(y)^2 < 16

Step-by-step explanation:

The equation of a circle is (x-h)^2+(y-k)^2 = r^2

We are outside the yellow circle  The yellow circle has a radius of 6 and a center at (2, -3)

(x-2)^2 +(y--3)^2 > 6^2

(x-2)^2 +(y+3)^2 > 36

We are also inside the blue circle which has a radius of 4 and a center of (4,0)

(x-4)^2 +(y-0)^2 < 4^2

(x-4)^2 +(y)^2 < 16

Answer:

D.) 36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2

Step-by-step explanation:

Edge 2022

Step-by-step explanation:

I do hope that you understand through the steps in the attachment, if not kindly reach out!

Answer:

a = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos60° = [tex]\frac{1}{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

a = 4[tex]\sqrt{3}[/tex]

9514 1404 393

Answer:

  73 ft²

Step-by-step explanation:

The ratio of areas is the square of the ratio of linear dimensions.

  smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)

  smaller area = 73 1/3 ft² ≈ 73 ft²

Answer:

Area of the smaller triangle = 73 square feet

Step-by-step explanation:

Area of the larger triangle = 165 square feet

Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]

[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]

Height = 22 ft

Since, both the triangles are similar.

By the property of similar triangles,

Corresponding sides of the similar triangles are proportional.

Let the height of smaller triangle = h ft

Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]

h = [tex]\frac{22\times 10}{15}[/tex]

h = 14.67 ft

Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]

                                              = 73.33

                                              ≈ 73 square feet

Answer:

44/3

Step-by-step explanation:

V=L*W*H

WH=22/3

V=2*(22/3)

Answer:

1.572

Step-by-step explanation:

For a standard normal distribution,

P(z > c) = 0.058

To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;

Using technology or table,

Zscore equivalent to P(Z > c) = 0.058 is 1.572

Hence, c = 1.572

Answer:

x = 15

Step-by-step explanation:

Pytago: a^2 + b^2 = c^2

x = [tex]\sqrt{25^{2} -20^{2} }[/tex] = 15

9514 1404 393

Answer:

  √3

Step-by-step explanation:

The ratio of the short sides to the hypotenuse in an isosceles right triangle is ...

  1 : 1 : √2

This means ...

  p·√2 = √6

  p = (√6)/(√2) = √(6/2)

  p = √3

Answer:

616.2442

area to the nearest whole number=616

Step-by-step explanation:

using formula 1/2absinx

where a =44,b=29 ,x=105

1/2x44x29xsin105

44x29=1276

1276÷2=638

638 x sin 105

the sin of 105 is 0.9659

if u are using a four figure table where u can't find 105 under sin of angle

u simply subtract 105 from 180=75

638 x 0.9659 =616.2442

approx.616

Answer:

t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks

S = V * t

V = S / t = 20 mi * 5280 ft/mi / 2800  sec  = 37.7 ft/sec

Since 88 ft/sec = 60 mph

the speed is 60 * 37.7 / 88 = 25.7 mph

Answer:

The point estimate of the proportion of the population that would provide Yes responses is 0.28.

Step-by-step explanation:

Point estimate of the proportion of the population that would provide Yes

The sample proportion of yes responses.

In the sample:

112 yes responses in the sample of 400, so:

[tex]p = \frac{112}{400} = 0.28[/tex]

The point estimate of the proportion of the population that would provide Yes responses is 0.28.

Answer:

Option (2)

Step-by-step explanation:

Let the savings of Joel = $y

And the savings of Matt = $x

They jointly save at least $50 to buy a special present.

Therefore, equation for this condition will be,

x + y ≥ 50 --------(1)

Joel saves twice as much as Matt.

Equation for this condition will be,

y = 2x ------ (2)

By substituting the value of 'y' in the equation,

x + 2x ≥ 50

Therefore, Option (2) will be the answer.

Answer:

A)

Step-by-step explanation:

the solution of a squared equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = 8

c = 22

x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =

= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =

= -4 ± sqrt(-6) = -4 ± i×sqrt(6)

Answer: I think the answer is A

Step-by-step explanation:

Answer:

L(x)=-4x+9

L(2.1)=0.6

Step-by-step explanation:

It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.

Theb use this to estimate f(2.1).

To find slope of tangent line, we must differentiate and then plug in 2 for x.

f'(x)=0-2x by constant and power rule.

f'(x)=-2x

So the slope of the tangent line is -2(2)=-4.

A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.

f(2)=5-(2)^2

f(2)=5-4

f(2)=1

So let's rephrase the question a little.

What's the equation for a line with slope -4 and goes through point (2,1).

Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.

Plug in our information: y-1=-4(x-2).

Distribute: y-1=-4x+8

Add 1 on both sides: y=-4x+9

Let's call this equation L(x), an expression to approximate value for f near x=2.

L(x)=-4x+9

Now the appropriation at x=2.1:

L(2.1)=-4(2.1)+9

L(2.1)=-8.4+9

L(2.1)=0.6

If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.

Answer:

A. x = 1/2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4x² + 3 = 4x + 2

Step 2: Solve for x