Four people recorded the number of minutes they exercised today. Mackenzie exercised for 3 as many minutes as Brinley. Brinley exercised for 17 fewer minutes than Ariana. Ariana exercised for 3 times as many minutes as Seth Together, Ariana and Mackenzie exercised for 20 more minutes than Brinley and Seth. Let z represent the number of minutes Seth exercised.​

Answer:

95% confidence interval for the mean daily sugar intake of residents in Durham County using this data

(35.9573, 38.8427)

Lower limit = 35.9573

Step-by-step explanation:

Step(i):-

Given that the size of the sample 'n' = 35

Given that the mean of sample x⁻ = 37.4gms

Given that the standard deviation of the sample 'S' = 4.2 gms

Level of significance = 0.05

Degrees of freedom

γ = n-1 = 35-1 = 34

t₀.₀₅ = 2.0322

Step(ii):-

95% confidence interval for the mean daily sugar intake of residents in Durham County using this data

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

[tex](37.4 - 2.0322 \frac{4.2}{\sqrt{35} } , 37.4 + 2.0322 \frac{4.2}{\sqrt{35} } )[/tex]

(37.4 - 1.4427 , 37.4+1.4427)

(35.9573, 38.8427)

Final answer:-

Lower 95% confidence interval for the mean daily sugar intake of residents in Durham County using this data

Lower limit = 35.9573

Answer:

113 degrees

its really hard to explain it on this app

Answer:

0.0475

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

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

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

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In a large company, the proportion of employees who were promoted during the last year was 0.10.

This means that [tex]p = 0.1[/tex]

100 employees

This means that [tex]n = 100[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 100*0.1 = 10[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.1*0.9} = 3[/tex]

What is the probability that at least 15 of them were promoted during the last year?

This is [tex]P(X \geq 15)[/tex], which is 1 subtracted by the pvalue of Z when X = 15. So

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

[tex]Z = \frac{15 - 10}{3}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a pvalue of 0.9525

1 - 0.9525 = 0.0475.

0.0475 is the answer.

Answer:

A

Step-by-step explanation:

Given

P(t) = 60 [tex](3)^{\frac{t}{2} }[/tex]

Then

P(1) = 60 × [tex]3^{\frac{1}{2} }[/tex] = 60[tex]\sqrt{3}[/tex]

P(2) = 60 × 3 = 180

P(3) = 60 × [tex]3^{\frac{3}{2} }[/tex] = 60 ×[tex]\sqrt{3^{3} }[/tex] = 60 × 3[tex]\sqrt{3}[/tex] = 180[tex]\sqrt{3}[/tex]

P(4) = 60 × 3² = 60 × 9 = 540

P(5) = 60 × [tex]3^{\frac{5}{2} }[/tex] = 60 × [tex]\sqrt{3^{5} }[/tex] = 60 × 9[tex]\sqrt{3}[/tex] = 540[tex]\sqrt{3}[/tex]

P(6) = 60 × 3³ = 60 × 27 = 1620

From these 6 results we see that

P(3) = 3 × P(1)

P(4) = 3 × P(2)

P(5) = 3 × P(3)

P(6) = 3 × P(4)

The predicted number of organisms triples every 2 days → A

Answer:

Step-by-step explanation:

That line that separates the triangle vertically is an angle bisector. That creates a ratio between the resulting 2 triangles:

[tex]\frac{6}{3x-12} =\frac{14}{21}[/tex] and cross multiply:

14(3x - 12) = 21(6) and

42x - 168 = 126 and

42x = 294 and

x = 7

Answer:

180 seconds

Step-by-step explanation:

1 minute = 60 seconds

120 * 3 = 360

60 * 3 = 180

Answer:

5,000

Step-by-step explanation:

it cant be 400 because the 4 in 5,421 is going to turn into a zero and everything behind that zero is a 0 as well and the thousand place is before the 0 so it stays the same

Answer:

38.5cm³

Step-by-step explanation:

1ml = 1cm³

38.5ml = 38.5cm³

Answer:

60.5

Step-by-step explanation:

assuming that each small squares is 1 × 1

[tex]\frac{1}{2} \times base \times height\\\\\frac{1}{2} \times 11 \times 11\\ \\\frac{121}{2}\\\\60.5 unit ^2[/tex]

Answer:

6

Step-by-step explanation:

8⅓% of 72

Change 8⅓% to an improper fraction, to get.

25/3% × 72

= (25/3)÷(100)×72

= (25/3)×(1/100)× 72

= (25/300) × 72

= 1800/300

= 6

The value of [tex]8\frac{1}{3}[/tex]% of 72 is 600.

Given that, [tex]8\frac{1}{3}[/tex]% of 72.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Now, [tex]8\frac{1}{3}[/tex]% of 72

25/3 × 72

= 25 × 24

= 600

Therefore, the value of [tex]8\frac{1}{3}[/tex]% of 72 is 600.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ2

Step-by-step explanation:

[tex]x = 10 \\ \\ y = 10 \sqrt{2} \\ \\ \cos(45) = \frac{ \sqrt{2} }{2} [/tex]

Answer:

x = 4

Step-by-step explanation:

To find x, plug in 14 into the function

f(x) = 3x + 2

14 = 3x + 2

Solve for x

14 = 3x + 2

12 = 3x

4 = x

So, the answer is x = 4

Answer:

The vertex of the graph is at (0,12)

The direction the graph opens is upward.

Step-by-step explanation:

Answer:

The vertex is (0,12)

The graph opens in a upward direction

Step-by-step explanation:

I got this correct on my test, hope this helped

Answer:

middle and right pictures are correct answer

Step-by-step explanation:

answer attached

The Figure 2 and 3 shows that XY tangent to circle C.

Tangent is a line that touches the circle and passes through at a touching point.

Need to prove that xy is a tangent line on the circle.

The circle of radius r and center z.

Sine the tangent of the circle and radius of the circle meet at 90 degrees.

Hence, a right-angle triangle is formed so we can apply the Pythagoras theorem.

Here,

xz = 7 cm

xy = 10 cm

Then

10² = 7² + b²

b² = 100 - 49

b² = 51

Hence, the first one doesn't show the  XY tangent to circle C.

Similalry for the rest two figures,

When a segment is tangent to a circle, it is perpendicular to the radius.

Therefore, Figure 2 and 3 shows that XY tangent to circle C.

More about Tangent link is given below.

brainly.com/question/1503247

#SPJ2

Step-by-step explanation:

We need to find the area of the shaded region. We see that the region next to that has a central angle of 120°. Also we know that angle in a straight line is 180° . So the measure of central angle of that shaded region will be 180° - 120° = 60° . Now we can use the formula of area of sector to find out the area of the shaded region.

[tex]\tt\to Area = \dfrac{\Theta}{360^o}\times \pi r^2 \\\\\tt\to Area = \dfrac{60^o}{360^o}\times \pi (8cm)^2 \\\\\tt\to Area =\dfrac{\pi \times 64}{6}cm^2\\\\\to\boxed{\orange{\tt Area_{(Shaded)}= 10.66\pi cm^2}}[/tex]

Answer:

y= -41

Slope= -1

Step-by-step explanation:

On the Y-axis put a point on -41. After you did that do down one unit and right one unit. Repeat this step below the Y-axis. Above the Y-axis you do the opposite. Go up one unit and left one unit. Repeat this step above the Y-axis. Hope you understood me :)

Answer:

$3,573.60

Step-by-step explanation:

.043 x (15300 - 10100) = 223.60

223.60 + 3350.00 = 3573.60

Answer:

Top left

Step-by-step explanation:

It’s the only one with a data point very far from the rest

Answer:

its diff for all of is but it deff right

Step-by-step explanation:

k12 right

Answer:

Step-by-step explanation:

1. Rotate 90° counterclockwise about the origin and then translate 5 units left.

2. Reflect across the y-axis and then rotate clockwise 180° about the origin.

3. Rotate 180° about the origin.

4. Rotate 90° clockwise about the origin and then translate 1 unit right and 5 units up.

Answer:

Step-by-step explanation:

X-intercepts are: (-10,-5,0,5,10)

Y-intercepts are: (-32,-24,-16,-8,0)

Answer:

-3/4

Step-by-step explanation:

y2 - y1 divided by x2 - x1 so you would do 2 - (-1) divided by 1 - 5

simplified is

3 divided by -4 or just -3/4

Answer: 8 x 24 divided by 2 and 8

Step-by-step explanation: