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3 years ago

Find the exact values of the following, giving your answers as fractions.

Mathematics

2 answers:

Stella [2.4K]3 years ago

7 0

Answer:

1/9
1/64
64

Step-by-step explanation:

The applicable rule of exponents is ...

a^(-b) = 1/(a^b)

Of course, an exponent is used to signify repeated multiplication.

3^(-2) = 1/3^2 = 1/(3·3) = 1/9

4^(-3) = 1/4^3 = 1/(4·4·4) = 1/64

2^6 = 2·2·2·2·2·2 = 64

9966 [12]3 years ago

4 0

Answer:

1/9 1/64 1/64

Step-by-step explanation:

to get full marks on mathswatch.

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A college entrance exam company determined that a score of 24 on the mathematics portion of the exam suggests that a student is

seraphim [82]

Answer:

a) The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at 0.01% level of significance

They score is above 24 on the math portion of the exam

b)

Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

Alternative Hypothesis: H₁: μ ≠ 24

Step-by-step explanation:

Step(i):-

Given random sample 'n' = 250

Given data sample mean x⁻ = 24.5

Standard deviation = 3.3

Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

Alternative Hypothesis: H₁: μ ≠ 24

test statistic

$Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{24.5 - 24}{\frac{3.3}{\sqrt{250} } } = \frac{0.5}{0.2087} = 2.397$

a) 99% or 0.01% level of significance

Level of significance ∝ = 0.01

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} =2.576$

The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at 0.01% level of significance

They score is above 24 on the math portion of the exam

b) 95% or 0.05% level of significance

Level of significance ∝ = 0.05

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96$

The Z -value 2.397 > 1.96 at 95% or 0.05% level of significance

Null hypothesis is Rejected at 0.05% level of significance

They score is below 24 on the math portion of the exam

6 0

2 years ago

What is the slope of 2x-3

dalvyx [7]

2 is the slope of 2x-3

6 0

2 years ago

Help with his long question

lana [24]

4x³=756
x³=189
x=3 ³√7 should be acceptable
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3 0

3 years ago

On Tuesday the Soto salad restaurant served 6 1/2 cups of Italian salad dressing. If the restaurant serves 1/4 cup of dressing w

Black_prince [1.1K]

Answer:

26 salads were ordered with Italian dressing

Step-by-step explanation:

Here, we want to know the number of salads ordered with Italian dressing;

To find the number of salads with Italian dressing, we shall need to divide the number of cups of italian salad dressing served by the number of cups of dressing served with each salad

Mathematically, that would be;

6 1/2 divided by 1/4

= 13/2 divided by 1/4

= 13/2 * 4/1 = 26

5 0

3 years ago

Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units ass

In-s [12.5K]

Answer:

is an attachment

test statistic = 9.87

p value is less than 0.01

Not all means of the three assembly methods are equal

Step-by-step explanation:

the anova table is an attachment

total number of methods = k = 3

number of observations n = 30

for treatment, df = 3-1 = 2

for error, df = 30 -3 (n-k) = 27

sst = 10800, sstr = 4560, sse = 10800-4560 = 6240

we find the mean of squares for error

sse/df of error = 6240/27 = 231.11

mean of squares for treatment = 4560/2 = 2280

test stat

F = 2280/231.11

= 9.8654

using f distribution table;

alpha = 0.05

df = 2 , 27

we get 3.35

h0; no difference in mean

h1; there is difference

9.87 > 3.35 so we reject H0, there is difference in means. all are not equal.

pvalue calculation

using excel,

FDIST(9.8654, 2, 27) = 0.0006078

p value is less than 0.01

we conclude that a. Not all means of the three assembly methods are equal

3 0

3 years ago