What is the slope of the line

Mrs. Bautista invested Php2700.00 part at 8% and the rest at 11% .How musch did she invest at each rate if her total annual inco

Margarita [4]

Answer:

The answer to the question is

She invested

Php2700.00 at 8 % and

Php 20,400.00 at 11 %

Step-by-step explanation:

To solve the question we note that

Simple interest is given by $\frac{P*R*T}{100}$ where

P= Principal, R = Rate and T = Time

If we call the first part P₁, T₁, and R₁ and the second part

P₂, T₂, and R₂

Then ${P_1*(1+R_1*T_1}) +{P_*(1+R_2*T_2}) = 2460.00$

= 2700×0.08×1 + P₂×0.11×1 = 2460 which gives

2244÷0.11 = P₂ or P₂ = Php 20,400.00

That is she invested

Php2700.00 at 8 % and

Php 20,400.00 at 11 %

5 0

3 years ago

Which of the following correctly expresses the number below in scientific notation?

Dafna11 [192]

The answer is E. $7.09*10^5$

6 0

3 years ago

g A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is cha

leva [86]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=410$ represent the number of people indicating that their financial security was more than fair for the recent year

$X_{2}=245$ represent the number of people indicating that their financial security was more than fair for the year before

$n_{1}=1000$ sample 1 selected

$n_{2}=700$ sample 2 selected

$p_{1}=\frac{410}{1000}=0.410$ represent the proportion estimated of indicating that their financial security was more than fair this year

$p_{2}=\frac{245}{700}=0.35$ represent the proportion estimated of indicating that their financial security was more than fair the year before

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+245}{1000+700}=0.385$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

7 0

3 years ago

The equation r(t)= (2t)i + (2t-16t^2)j is the position of a particle in space at time t. Find the angle between the velocity and

ankoles [38]

Answer:

The answer is 135 degrees.

Step-by-step explanation:

As we are given the position. If we take the <u>derivative</u>, we get the velocity vector. If we take the <u>derivative</u> again, we find the acceleration vector of the particle.

$r(t)=(2t)i+(2t-16t^{2})j$