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3 years ago

The area of a rectangle patio is 12-3/8 square meters. The width of the patio is 2-3/4 meters. What is the length?

1 answer:

6 0

Area=length x width
A=lw
A=12 3/8
l=x
w=2 3/4

first, make your mixed numbers into improper fractions
12 3/8 --> 99/8
2 3/4 --> 11/4

then, set equal denominators

99/8 and 22/8

99/8=22/8x --plug in values
99/22=x --divide both sides by 22/8

convert improper fraction to mixed number
99/22 --> 4 11/22 --> 4 1/2

therefore, the length is 4 1/2 meters

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An angle measures 14° less than the measure of its complementary angle. What is the measure of each angle?

zmey [24]

(180-14):2= 166:2= 83° (smaller angle)
(180-14):2+14= 166:2+14= 83+14= 97° (bigger angle)

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2 years ago

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Which expression has a value of 17?

Ivahew [28]

The second choice is the answer

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2 years ago

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Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet,

Ivan

Answer:

15 feet

Step-by-step explanation:

Quadrilateral ABCD has a scale facter of 2.5 over the quadrilateral EFGH. The order of ABCD is 60, 40, 30, and x, EFGH has y, z, 12, and 6.

6 times the scale factor of 2.5 is 15, the answer.

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3 years ago

A college counselor is interested in estimating how many credits a student typically enrolls in each semester. The counselor dec

Ket [755]

Answer:

(a) The usual load is not 13 credits.

(b) The probability that a a student at this college takes 16 or more credits is 0.1093.

Step-by-step explanation:

According to the Central limit theorem, if a large sample (n ≥ 30) is selected from an unknown population then the sampling distribution of sample mean follows a Normal distribution.

The information provided is:

$Min.=8\\Q_{1}=13\\Median=14\\Mean=13.65\\SD=1.91\\Q_{3}=15\\Max.=18$

The sample size is, n = 100.

The sample size is large enough for estimating the population mean from the sample mean and the population standard deviation from the sample standard deviation.

So,

$\mu_{\bar x}=\bar x=13.65\\SE=\frac{s}{\sqrt{n}}=\frac{1.91}{\sqrt{100}}=0.191$

(a)

The null hypothesis is:

H₀: The usual load is 13 credits, i.e. μ = 13.

Assume that the significance level of the test is, α = 0.05.

Construct a (1 - α) % confidence interval for population mean to check the claim.

The (1 - α) % confidence interval for population mean is given by:

$CI=\bar x\pm z_{\alpha/2}\times SE$

For 5% level of significance the two tailed critical value of z is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Construct the 95% confidence interval as follows:

$CI=\bar x\pm z_{\alpha/2}\times SE\\=13.65\pm (1.96\times0.191)\\=13.65\pm0.3744\\=(13.2756, 14.0244)\\=(13.28, 14.02)$

As the null value, μ = 13 is not included in the 95% confidence interval the null hypothesis will be rejected.

Thus, it can be concluded that the usual load is not 13 credits.

(b)

Compute the probability that a a student at this college takes 16 or more credits as follows:

$P(X\geq 16)=P(\frac{X-\mu}{\sigma}\geq \frac{16-13.65}{1.91})\\=P(Z>1.23)\\=1-P(Z$

Thus, the probability that a a student at this college takes 16 or more credits is 0.1093.

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2 years ago

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Graph the quadratic functions y=-2xandy=-2x2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shap

dedylja [7]

Y = -2x^2

h = Xv = -B/2A = 0/-4 = 0.

k = -2*0^2 = 0.

V(0,0).

Use the following points for graphing:

Y = -2x^2.

(x,y)

(-2,-8)

(-1,-2)

V(0,0)

(1,-2)

(2,-8)

Y = -2x^2 + 4.

h = Xv = -B/2A = 0/-4 = 0.

k = Yv = -2*0^2 + 4 = 4.

V(0,4).

(-2,-4)

(-1,2)

V(0,4)

(1,2)

(2,-4)

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2 years ago