Question 10

A bank loaned out $29,000, part of it at the rate of 13% annual interest, and the rest at 4% annual interest.

The total interest earned for both loans was $2,195.00. How much was loaned at each rate?

Answer:

s must be 21 and r is 20

Step-by-step explanation:

Represent the two numbers using variables r and s.

Then r + s = 41, and r = s - 1

Substituting the 2nd equation for r into the first equation, we get:

s - 1 + s = 41, or 2s = 42.  Then s must be 21 and r is 20.

Answer: C

Step-by-step explanation:

Since the sides are marked with the little lines, you know they are congruent with each other. Since the sides are congruent, you know the hypotenuse will be congruent.

You can argue that these triangles are similar, but the difference is that similar triangles are the same shape, but not the same size. These triangles are congruent because they are the same size and shape. Therefore, the hypotenuse is congruent.

Answer:

153

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

Assuming these rectangles are similar, you can set up a proportion like this:

[tex]\frac{15}{10} =\frac{x}{4}[/tex]

→Cross multiply:

[tex]\frac{60}{10x}[/tex]

→Divide 60 by 10:

x = 6

Answer:

$190,000

Step-by-step explanation:

discount = x

original price = $200,000

discount% = 5%

x/200,000 = 5/100

x · 100 = 5 · 200,000

100x = 1,000,000

100x/100 = 1,000,000/100

x = 10,000

Sale price: $200,000 - $10,000 = $190,000

Answer:

B

Step-by-step explanation:

OP = OQ

Answer:

B

Step-by-step explanation:

Look at the shape closely observe the following the imaginary lines;

OC = OA , OB = OD {these is the raduis of the circle;

note also line CQ = CD { the perpendicular line bisects line CD in two equal halves;

Similarly ;

note also line AP= PB { the perpendicular line bisects line OP in two equal halves}

Hence;

OP is congruent to the OQ

In maths we say something is congruent when they are the same shape and have same angles but we are allowed to flip it's side.

Answer:

= 180 yd^3

Step-by-step explanation:

The volume of a triangle prism is

V= Bh where B is the area of the base

B = area of the triangle

   = 1/2 *8* 5

    = 20 yd^2

V = 20 yd^2 * 9 yd

  = 180 yd^3

Answer:

i

Step-by-step explanation:

It's imaginary, or it can also be referred to as i.

Answer:

90% confidence interval for the true population mean textbook weight is [35.79 ounces , 38.21 ounces].

Step-by-step explanation:

We are given that you measure 50 textbooks' weights, and find they have a mean weight of 37 ounces.

Assume the population standard deviation is 5.2 ounces.

Firstly, the Pivotal quantity for 90% confidence interval for the population mean is given by;

                           P.Q. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean weight = 37 ounces

           [tex]\sigma[/tex] = population standard deviation = 5.2 ounces

           n = sample of textbooks = 50

           [tex]\mu[/tex] = true population mean textbook weight

Here for constructing 90% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 90% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5%

                                            level of significance are -1.645 & 1.645}  

P(-1.645 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.645) = 0.90

P( [tex]-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90

P( [tex]\bar X -1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X +1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90

90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X -1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X +1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                          = [ [tex]37-1.645 \times {\frac{5.2}{\sqrt{50} } }[/tex] , [tex]37+1.645 \times {\frac{5.2}{\sqrt{50} } }[/tex] ]

                                          = [35.79 , 38.21]

Therefore, 90% confidence interval for the true population mean textbook weight is [35.79 ounces , 38.21 ounces].

Answer:

Step-by-step explanation:

For military scholarship,

Mean, x1 = (850 + 925 + 980 + 1080 + 1200 + 1220 + 1240 + 1300)/8

x1 = 1099.375

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

n1 = 8

Summation(x - mean)² = (850 - 1099.375)^2 + (925 - 1099.375)^2 + (980 - 1099.375)^2 + (1080 - 1099.375)^2 + (1200 - 1099.375)^2 + (1220 - 1099.375)^2 + (1240 - 1099.375)^2 + (1300 - 1099.375)^2 = 191921.875

Standard deviation, s1 = √(191921.875/8

s1 = 154.89

For no military scholarship,

Mean, x2 = (820 + 850 + 980 + 1010 + 1020 + 1080 + 1100 + 1120 + 1120 + 1200 + 1220 + 1330)/12

x2 = 1070.83

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

n2 = 12

Summation(x - mean)² = (820 - 1070.83)^2 + (850 - 1070.83)^2 + (980 - 1070.83)^2 + (1010 - 1070.83)^2 + (1020 - 1070.83)^2 + (1080 - 1070.83)^2 + (1100 - 1070.83)^2 + (1120 - 1070.83)^2 + (1120 - 1070.83)^2 + (1200 - 1070.83)^2 + (1220 - 1070.83)^2 + (1330 - 1070.83)^2 = 238091.6668

Standard deviation, s2 = =√(238091.6668/12

s2 = 140.86

Part A)

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean score of students with military scholarship and μ2 be the mean score of students without military scholarship.

The random variable is μ1 - μ2 = difference in the mean score between students with military scholarship and without military scholarship

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (1099.375 - 1070.83)/√(154.89²/8 + 140.86²/12)

t = 0.42

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [154.89²/8 + 140.86²/12]²/[(1/8 - 1)(154.89²/8)² + (1/12 - 1)(140.86²/12)²] = 21644133.914878543/1533280.3458504018

df = 14

We would determine the probability value from the t test calculator. It becomes

p value = 0.68

Since alpha, 0.05 < than the p value, 0.68, then we would fail to reject the null hypothesis. Therefore, at a significance level of 5%, these data do not provide convincing evidence of a difference in SAT scores between students with and without a military scholarship

Part B)

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (8 - 1) + (12 - 1) = 18

z = 2.101

x1 - x2 = 1099.375 - 1070.83 = 28.545

Margin of error = 2.101√(154.89²/8 + 140.86²/12) = 143.3

The 95% confidence interval is 28.545 ± 143.3

Answer:

[tex]h \geq 2\frac{2}[3}[/tex]

Step-by-step explanation:

We solve the inequality similarly to how we would solve an equalitu.

[tex]6h - 5(h-1) \leq 7h - 11[/tex]

[tex]6h - 5h + 5 \leq 7h - 11[/tex]

[tex]h - 7h \leq -11 - 5/[/tex]

[tex]-6h \leq -16[/tex]

Multiplying everything by -1

[tex]6h \geq 16[/tex]

Simplifying by 2

[tex]3h \geq 8[/tex]

[tex]h \geq \frac{8}{3}[/tex]

8 divided by 3 is 2 with rest two. So as a improper fraction, the answer is:

[tex]h \geq 2\frac{2}[3}[/tex]

Answer:

[8,

3

Step-by-step explanation:

Answer:

C. 4√5i

Step-by-step explanation:

on edge

please vote brainliest i have never gotten it before

Answer:

1. all real numbers less than or equal to 4 = </= 4.

Answer = YES!

2. all real numbers less than or equal to -3 = </= -3.

Answer = YES!

3. all real numbers greater than or equal to 4 = >/= 4

Answer = YES!

4. all real numbers greater than or equal to -3 = >/= -3

Answer = NO!

Step-by-step explanation:

1. all real numbers less than or equal to 4 = </= 4.

1 + 1 = 2

1 + 2 = 3

2 + 2 = 4

2. all real numbers less than or equal to -3 = </= -3.

1 - 1 = 0

1 - 2 = -1

1 - 3 = -2

1 - 4 = -3

3. all real numbers greater than or equal to 4

1 + 1 = 2

1 + 2 = 3

1 + 3 = 4

1 + 4 = 5

4. all real numbers greater than or equal to -3

1 - 1 = 0

1 - 2 = -1

1 - 3 = -2

1 - 4 = -3

Answer:

The range is all real numbers less than or equal to 4

Step-by-step explanation:

took the test on edge

Answer:

$5350

Step-by-step explanation:

see attachment

Answer:

Its 53.50

Step-by-step explanation:

Answer:

domain: (-∞,∞)

range [-3,∞)

Step-by-step explanation:

The domain is the values that x can take

X can be any value so the domain is all real numbers

The range is the values that y can take

The minimum value is -3

The range is y ≥ -3

Answer:

648

Step-by-step explanation:

Number of Assaults, n(A)=430

Number of Robberies, n(R)=146

Number of Drug Sales Offenses, n(D)=131

Number involved in both assault and robbery= [tex]n(A\cap R)=26[/tex]

Number involved in both assault and drug sales= [tex]n(A\cap D)=33[/tex]

Therefore, to find the greatest possible number of offenders for May who satisfy these statistics, we remove the number of those who were involved in more than one crime.

This gives us:

[tex]=n(A)+n(R)+n(D)-n(A\cap R)-n(A\cap D)\\=430+146+131-26-33\\=648[/tex]

The greatest possible numbers of offenders in May is 648.

Answer:

1.12

2.85

3.60

Step-by-step explanation:

1.

if m = 12 you solve by dividing 144/12

144/12 = 12

2.

when m = 11 you solve by computing 7(11) + 8

7(11) = 77 so you solve from there 77 + 8 which equals 85

3.

When g = 4 you solve my multiplying 15(4)

15(4) = 60

Answer:

first question: 12

second question: 85

third question: 60

Step-by-step explanation:

first question: plug in 12 for m and you would get 144/12 which equals 12.

Second question: plug in 11 for m and you have 7(11) + 8.

77+8 = 85

third question: plug in 4 for g and you have 15(4)

15 x 4 = 60.

*parentheses mean multiplication when next to a number

ex: 7(11)

not ex: 3 + (2/3) since it isn't directly next to the first number, instead its adding

Answer:

3/8

Step-by-step explanation:

45/72=5/8

(5/8)+x=72/72

x=1-(5/8)

x=3/8

Answer:

a) Residents of San Antonia, Texas

b) Response variable

c) Explanatory variable

d) Observational study

e) Response bias

f) The appropriate scope of interest is the " relationship between age and the weekly average usage of local parks in San Antonia"

Step-by-step explanation:

a) In this study, the objects or entities on which observation is done are the residents of San Antonia, hence they are the observational units.

b) In this observation, the number of visits per week is the response variable because it is the outcome of the observation. It is a dependent variable that varies due to variation in the ages.

c) Age is the variable that helps to predict the average number of visits to the park, it can then be called the predictor variable. It is independent of any external variable.

d) This is an observational study because it is meant to observe the relationship between the ages and the average number of visits to the park per week. The variables are not randomly assigned.

e ) The type of bias that is most concerning in this study is response bias. This is because it is a paper survey and their can be invalid responses either due to unfaithfulness or ignorance of the respondents.

f) The appropriate scope of the inference in this study is the relationship between the ages and the weekly average usage of local parks in San Antonia.

Answer:

[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.

Step-by-step explanation:

Information given

[tex]\bar X=98.2[/tex] represent the sample mean

[tex]\sigma=0.62[/tex] represent the population standard deviation

[tex]n=60[/tex] sample size  

[tex]\mu_o =98.6[/tex] represent the value that we want to test

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the true mean is equal to 98.6 F, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 98.6[/tex]  

Alternative hypothesis:[tex]\mu \neq 98.6[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

The degrees of freedom, on this case:  

[tex]df=n-1=60-1=59[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.

72+72+36= 144+36= 180

Answer:

Area of the figure = 176 m²

Step-by-step explanation:

Area of Rectangle = Length × Width

Dividing the whole figure

Rectangle 1:

6 × 18 = 108 m²

Rectangle 2 :

10 × 6 = 60 m²

Rectangle 3:

2 × 4 = 8 m²

Adding All

Area of the figure = 108 + 60 + 8

Area of the figure = 176 m²

Answer:

  10

Step-by-step explanation:

Using the distance formula, the distance is ...

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((-2-4)^2 +(-4-4)^2) = √((-6)^2 +(-8)^2) = √(36 +64)

  d = √100 = 10

The distance between the two points is 10 units.

Answer:

The answer is 4

Step-by-step explanation:

1.5(4+4)-3= 9

4.5(4-2)=9

9=9

Answer:

[tex]x=4[/tex]

Explanation:

[tex]1.5x+6+-3=4.5x+-9\\1.5x+3=4.5x-9\\-3x+3=-9\\-3x=-12\\x=4[/tex]

Answer:

11.90% probability that the mean profit for the sample was between 0 million and 5.1 million

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 6.54, \sigma = 10.45, n = 73, s = \frac{10.45}{\sqrt{73}} = 1.2231[/tex]

In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between 0 million and 5.1 million?

This is the pvalue of Z when X = 5.1 subtracted by the pvalue of Z when X = 0. So

X = 5.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5.1 - 6.54}{1.2231}[/tex]

[tex]Z = -1.18[/tex]

[tex]Z = -1.18[/tex] has a pvalue of 0.1190

X = 0

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0 - 6.54}{1.2231}[/tex]

[tex]Z = -5.35[/tex]

[tex]Z = -5.35[/tex] has a pvalue of 0

0.1190 - 0 = 0.1190

11.90% probability that the mean profit for the sample was between 0 million and 5.1 million

Answer:

0.35

Step-by-step explanation:

.5x.7

Answer:

12.5 hours

Step-by-step explanation:

The data which represents the battery life, in hours, experienced by six users is given below:

10 14 14 16 13 8

To determine the point estimate for the web browsing battery life of the iPad, we find the mean number of hours.

[tex]Mean=\dfrac{10+14+14+16+13+8}{6} \\\\=\dfrac{75}{6} \\\\=12.5[/tex]

The point estimate for the web browsing battery life of the iPad is: 12.5 hours

Answer:

Hi there!

The correct answer is C.

Step-by-step explanation:

A polynomial identity  are equations that are true for all possible values of the variable. For example, x²+2x+1=(x+1)² is an identity.

Answer:

y =34

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

63+ 2y+ y+15 = 180

Combine like terms

78+ 3y = 180

Subtract 78 from each side

78+3y-78 = 180-78

3y = 102

Divide each side by 3

3y/3 = 102/3

y =34

Answer:

[tex]y = 34[/tex]

Step-by-step explanation:

Sum of the angles in a triangle is 180 degrees

[tex]2y + 63 + y + 15 = 180 \\ 3y + 63 + 15= 180 \\ 3y +7 8 = 180 \\ 3y = 180 - 78 \\ 3y =10 2 \\ \frac{3y}{3} = \frac{102}{3} \\ y = 34 [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

x = (rs + t)/(r-s)

Step-by-step explanation:

r(x - s) = sx + t

rx - rs = sx + t

rx - sx = rs + t

x(r - s) = rs + t

x = (rs + t)/(r-s)

The solution for x is x = (t + rs)/(r - s).

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

We can begin by simplifying the given equation:

First, solve the parenthesis,

r(x - s) = sx + t

Simplify, the equation, we get,

rx - rs = sx + t

rx - sx = t + rs

Take the like terms to one side, we get,

x(r - s) = t + rs

Now, solve for x, we get,

x = (t + rs)/(r - s)

Therefore, x is equal to (t + rs)/(r - s).

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ7

Answer:

amount of fabric to make the bag = 4 yards

Step-by-step explanation:

Tara has 1 3/5 yards of fabric . She needs extra 2 1/2 times the amount she have to make a shopping bag. The amount of fabric she needs to make the bag can be calculated as follows.

1 3/5 yards = 8/5 yards of fabrics

What she actually needs to make a shopping bag is two and half the amount she has . Mathematically, it can be express

2 1/2 × 8/5

Let us change 2 1/2 to improper fraction

amount of fabric to make the bag = 5/2 × 8/5

amount of fabric to make the bag = 40/10

amount of fabric to make the bag = 4 yards