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Art [367]
2 years ago
12

Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown.

Mathematics
2 answers:
PolarNik [594]2 years ago
5 0

Answer: 2

Step-by-step explanation: No explanation needed...

yuradex [85]2 years ago
5 0

Answer:

Step-by-step explanation:

8y +18 = 12y-108y +28 = 12y28 = 4yy = 28/4 = 7y = 7C is the answer

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Find the 1st , 2nd (median) and 3rd quartile of the set of numbers 6,8,2,6,7,9 ?
zubka84 [21]

Answer:

at first we put the numbers in order from least to greatest

2 , 6 , 6 , 7 , 8 , 9

1st quartile = 6

median = (6+7)/2 = 6.5

3rd quartile = 8

5 0
3 years ago
PLEASE HELP ME I BEG I WILL GIVE BRAINLIEST
ohaa [14]

Answer:

Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48

Standard deviation = √(summation(x - mean)²/n

n = 6

Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484

Standard deviation = √(0.1484/6

s = 0.16

Standard error = s/√n = 0.16/√6 = 0.065

Part B

Confidence interval is written as sample mean ± margin of error

Margin of error = z × s/√n

Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5

Therefore, z = 3.365

Margin of error = 3.365 × 0.16/√6 = 0.22

Confidence interval is 2.48 ± 0.22

Part C

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 2.3

For the alternative hypothesis,

H1: µ > 2.3

This is a right tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 6

Degrees of freedom, df = n - 1 = 6 - 1 = 5

t = (x - µ)/(s/√n)

Where

x = sample mean = 2.48

µ = population mean = 2.3

s = samples standard deviation = 0.16

t = (2.48 - 2.3)/(0.16/√6) = 2.76

We would determine the p value using the t test calculator. It becomes

p = 0.02

Assuming significance level, alpha = 0.05.

Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.

Step-by-step explanation:

7 0
3 years ago
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 220 feet of f
MrRa [10]

Answer:

6050 square feet

Step-by-step explanation:

Based on the diagram attached, the area which the available fencing can enclose will measure X x Y feet. As the total length of fencing available is 220 feet, the fenced perimeter must equal 220 feet

Y + 2X = 220

Y = 220 - 2X

Area of a rectangle is determined by multiplying the length of perpendicular sides:

Area = X*Y

Area = X(220 - 2X)

Area = 220X - 2X^{2}

The derivative of an equation determines the slope at any given point of that equation. At the maximum or minimum point of the equation, the slope will be zero. Therefore, differentiating the equation for area and equating it to zero will give the value of X where the area is maximum.

A simple variable can be differentiated using below concept:

f(a) = a^{b}

f'(a) = ba^{b-1}

Using the above concepts to differentiate Area and calculate X will give:

Area = 220X - 2X^{2}

Area' = 220 - 4X = 0

X = 55

Calculating Y:

Y = 220 - 2X

Y = 220 - 2(55)

Y = 110

Calculating Area:

Area = X*Y

Area = 55*110

Area = 6050\sqfeet

8 0
2 years ago
5cosx -2sin(x/2) +7=0<br>Help me to find x step by step<br>pls​
miskamm [114]

Answer:

x = 180

Step-by-step explanation:

First, you need to know

1. Double-angle formula:

cos(2x) = cos^{2}x - sin^{2}x

2. Pythagorean identity:

cos^{2}x + sin^{2}x = 1

Back to your problem, replacing the variable by the above:

5cosx-sin\frac{x}{2}+7 = 0

5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0 By Double-angle formula

5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0 By Pythagorean identity

Given y = \frac{x}{2}

5(1-2sin^{2}y) - 2siny + 7 = 0

10sin^{2}y+2siny-12=0

5sin^{2}y+siny-6=0

(5siny + 6)(siny - 1)=0, we know -1 < sinx < 1, for every x ∈ R

siny = 1, y =90

y = \frac{x}{2}

x = 180

8 0
3 years ago
Solve four square root of six plus eight square root of four and explain whether the answer is rational or irrational.
Inga [223]

Answer:

4\sqrt{6}+16

Step-by-step explanation:

Given the expression: 4\sqrt{6}+8\sqrt{4}

\sqrt{4}=2\\$Therefore, \\4\sqrt{6}+8\sqrt{4}  =4\sqrt{6}+8*2\\  =16+4\sqrt{6}

We can re-write the answer as:

4\sqrt{6}+16

The answer is irrational because the sum of a rational number and irrational number is an irrational number.

<u>The correct option is B.</u>

7 0
3 years ago
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