If something is proportional, as one value increases, the other increases at the same rate.

Write one and two fifths as a fraction only

Alchen [17]

What type of fraction?

Mixed Fraction/Number: 1 2/5.

Improper fraction: 7/5

6 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=f%20-%20354%20%3D%201221" id="TexFormula1" title="f - 354 = 1221" alt="f - 354 = 1221" align="

alukav5142 [94]

$f-354=1221$ add 354 to both sides

$f+354-354=1221+354\\\\\boxed{f=1,575}\to\boxed{D.}$

6 0

3 years ago

use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4

Firdavs [7]

The expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

The power-reducing formula, for cosine, is,

cos² θ = (1/2)[1 + cos 2θ].

In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.

We can do it as follows:

cos⁴ θ

= (cos² θ)²

= {(1/2)[1 + cos 2θ]}²

= (1/4)[1 + cos 2θ]²

= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}

= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)

= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]

= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8

= 3/8 + cos 2θ/4 + cos 4θ/8

= [ 3 + 2cos 2θ + cos 4θ]/8.

Thus, the expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

Learn more about reducing trigonometric powers at

brainly.com/question/15202536

#SPJ4

5 0

2 years ago

If Maria can read 8 pages in 40 minutes, how many pages can she read in 120 minutes?

yarga [219]

8/40=?/120 40x3=120 8x3=24 so 24 pages or 24/120

7 0

2 years ago

A person purchased a slot machine and tested it by playing it 1,137 times. There are 10 different categories of outcomes, includ

ivann1987 [24]

Answer:

$p_v= P(\chi^2_{9}>11.517)=0.2419$

And on this case if we see the significance level given $\alpha=0.1$ we see that $p_v>alpha$ so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.

Step-by-step explanation:

A chi-square goodness of fit test determines if a sample data obtained fit to a specified population.

$p_v$ represent the p value for the test

O= obserbed values

E= expected values

The system of hypothesis for this case are:

Null hypothesis: $O_i = E_i[/tex[Alternative hypothesis: [tex]O_i \neq E_i$

The statistic to check the hypothesis is given by:

$\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

On this case after calculate the statistic they got: $\chi^2 = 11.517$

And in order to calculate the p value we need to find first the degrees of freedom given by:

$df=n-1=10-1=9$ , where k represent the number of levels (on this cas we have 10 categories)

And in order to calculate the p value we need to calculate the following probability:

$p_v= P(\chi^2_{9}>11.517)=0.2419$

And on this case if we see the significance level given $\alpha=0.1$ we see that $p_v>alpha$ so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.

6 0

3 years ago