Sue invests £9000 in an account for one year.
At the end of the year, interest is added to the account.

Sue pays tax on this interest at a rate of 20%.
She pays £30.24 tax.

Work out the percentage interest rate for the account.

Answer:

[tex]1^x[/tex] is always 1, so [tex]1^x-1^x=0[/tex]

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dame grasias

si soi nuevo

Answer:

[tex]=210[/tex]

Step-by-step explanation:

[tex]7\times \left(-150\right)\div \left(10-10-5\right)\\Follow\:the\:PEMDAS\:order\:of\:operations\\\mathrm{Calculate\:within\:parentheses}\:\left(10-10-5\right)\::\quad -5\\10-10-5\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\\10-10=0\\=0-5\\=0-5\\=-5\\=7\times \left(-150\right)\div \left(-5\right)\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:7\times \left(-150\right)\div \left(-5\right)\::\quad 210\\7\times \left(-150\right)\div \left(-5\right)[/tex]

[tex]\mathrm{Apply\:rule\:}-a\div \left(-b\right)\:=\:a\div \:b\\-1050\div \left(-5\right)=1050\div \:5=210\\=210[/tex]

Answer:

210

Step-by-step explanation:

7×{(-150)÷(10-10-5)}

remove the opposites

7×{(-150)÷(-5)}

divide

7×30

multiply

210

Answer:

22.05

Step-by-step explanation:

Answer:

x=5/4

Step-by-step explanation:

First, plug in 1 for y. Since a common denominator for the right side is 3, multiply both sides by 3 to get 3=x+11/5. Then multiply both sides by 5 to get 15=5x+11. Subtract 11 on both sides to get 4=5x. Finally divide by 5 to get x by itself and get x = 5/4.

Answer: C,D are true

Step-by-step explanation:

Answer:

Step-by-step explanation:

C and D are both true the rest are false

Answer:

[tex]10\frac{2}{5}[/tex]

Step-by-step explanation:

[tex]7\frac{3}{5} + x = 18\\[/tex]

transformation : [tex]7\frac{3}{5} = \frac{(5*7) + 3}{5} = \frac{38}{5}[/tex]

[tex]\frac{38}{5} + x = 18\\\\x = 18 - \frac{38}{5} = \frac{(5*18) - 38}{5} = \frac{52}{5}[/tex]

[tex]\frac{52}{5} = 10\frac{2}{5}[/tex]

Answer:

[tex]10\frac{2}{5}[/tex]

Step-by-step explanation:

What should be add to [tex]7\frac{3}{5}[/tex]  to get [tex]18[/tex] ?

[tex]18-7\frac{3}{5}=\\ \\=17\frac{5}{5}-7\frac{3}{5}\\\\\\=(17-7)+(\frac{5}{5}- \frac{3}{5})\\ \\=10+\frac{2}{5}\\ \\=10\frac{2}{5}[/tex]

Explanation:

1. a) Null hypothesis: There is no statistically significant relationship between the mouse grimace scale and the amount of pain felt by mouse.

b) Alternate hypothesis: There is a statistically-significant relationship between the mouse grimace scale and the amount of pain felt by mouse.

2. Yes, because a statistically significant data implies that there is sufficient evidence to believe the study, based on the results of the findings.

3. No, since the variables are different in this case. Here we are dealing with a non-painful solution so there may be no sample correlation as extreme as that found in the original study.

4. Possibly, because every hypothesis is an assumption until it is proven. Thus, in every statistical research, there may be different findings.

Answer:

Convert the age to a z-score:

Step-by-step explanation:

Let X be the random variable with mean 27.2 and standard deviation 3.8.

Here, the observation, x is 24.

The z-score of the winner's age is -1.56.

A negative z-score indicates that the value is below the mean.

The age of the winner is not considered unusual.

A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.

It measures the unusual or extreme a particular data point is compared to the rest of the distribution

We have,

(a)

To transform the age of the winner into a z-score, we use the formula:

z = (x - μ) / σ

where x is the value we want to transform, μ is the mean, and σ is the standard deviation.

So,

Substituting the values given,

z = (22 - 27.3) / 3.4

z = -1.56

The z-score of the winner's age is -1.56.

(b)

A z-score represents the number of standard deviations a data point is from the mean.

In this case, the winner's age is 1.56 standard deviations below the mean age of the winners.

A negative z-score indicates that the value is below the mean.

(c)

Compare the z-score to a threshold value.

A commonly used threshold for unusual values is z = ±2.

If the absolute value of the z-score is greater than or equal to 2, then the value is considered unusual.

So,

The absolute value of the z-score is less than 2 (|z| < 2), which means that the age of the winner is not considered unusual in the context of the distribution of the ages of the winners.

Thus,

The z-score of the winner's age is -1.56.

A negative z-score indicates that the value is below the mean.

The age of the winner is not considered unusual.

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Answer:

Step-by-step explanation:

From the information given, their last meter reading was 123,692 and their present reading is 127,394. The difference between the last and the present meter reading is

127394 - 123692 = 3702

If the water meter measures its water usage in terms of 1 point in CCF, then the amount of CCF of water used is 3702. If the school is charged $0.36 per CCF of water, then for this usage, the charge would be

3702 × 0.36 = $1332.72

Therefore, it is false

Answer:

19.99

Step-by-step explanation:

First you would multiply .44 by 16 to get 7.04

then you would add 12.95 to get 19.99

Answer:

8

Step-by-step explanation:

1 quart=4 cups so 4x2=8

Answer:

$104430

Step-by-step explanation:

Let's recall the formula

PRT/100 = interest I

Where

P = principal/initial amount

R = rate

T= period or time

P =( 100*I)/(RT)

P =( 100*1320)/(15*(30/356))

P = 132000/1.264

P = $104430

Answer:

Option D

Step-by-step explanation:

A matched pairs t-test is appropriate for this experiment. It compares two means that are from the same individual; the before drug administration and the after drug administration. It compares the before-and-after observations on the same subjects.

The best and convincing statistical evidence of a change, on average, in blood pressure is the t test.

The test is one of the kinds of inferential statistics. It is deployed in decision making. As such, it involves the test to see if there is significant difference between the means of two groups, which may be related.

Hence, in this study, the best and convincing statistical evidence of a change, on average, in blood pressure is the t test.

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Answer:

all I see is a black image

Answer:

x = 23/5 and y = 7/20

Step-by-step explanation:

2x + 8y = 12 and 3x - 8y = 11 are two given equations

Now,

Step 1:

2x + 8y = 12 ...(1)

3x - 8y = 11 ...(2)

Step 2:

From equation (2) we get the value of x

i.e.,

3x - 8y = 11

3x = 8y + 11

x = 8y + 11/3

Step 3:

Now,

Put the value of x = 8y + 11/3 in equation (1) we get,

i.e.,

2x + 8y = 12

2(8y + 11/3) + 8y = 12

16y + 22/3 + 8y = 12

16y + 22 + 8y(3)/3 = 12

16y + 22 + 24y/3 = 12

16y + 24y + 22 = 12 * 3

40y = 36 - 22

40y = 14

y = 14/40

y = 7/20

Step 4:

Now,

Substitute the value of y = 7/20 in equation (2) we get,

i.e.,

3x - 8y = 11

3x - 8(7/20) = 11

3x - 56/20 = 11

3x - 14/5 = 11

3x = 11 + 14/5

3x = 11 * 5 + 14/5

3x = 55 + 14/5

3x = 69/5

x = 69/3 * 5

x = 23/5

Answer: B. -2x^4y^3

Step-by-step explanation:

Multiply the variables by each other.

-2x^3 * x = -2x^4

y * y^2 = y^3

Answer:

B) -2x4y3

Step-by-step explanation:

the answer is in the photos

Answer:

B. The graph cross the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10

Step-by-step explanation:

→Looking at the line as it increases, you can see that it intersects at the point of (0, 5) on the y-axis.

→The line on the graph is increasing from the point where x = -10, and stops at x = 2.

→The line then stays constant (basically meaning it doesn't increase/decrease, making it a horizontal line), strting from x = 2, to x = 10.

Looking at the points above, you can determine that the correct answer is "B. The graph cross the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10."

Answer:

=2v−20

Step-by-step explanation:

Let's simplify step-by-step.

v−2+v−18

=v+−2+v+−18

Combine Like Terms:

=v+−2+v+−18

=(v+v)+(−2+−18)

=2v+−20

Answer:

=2v−20

Step-by-step explanation:

[tex]5(2x - 4) = 2(4x + 2) \\ 10x - 20 = 8x + 4 \\ 2x = 24 \\ x = 12[/tex]

Answer:

[tex]y=32[/tex]

Step-by-step explanation:

[tex]\frac{7}{4}y=56\\\mathrm{Multiply\:both\:sides\:by\:}4\\4\cdot \frac{7}{4}y=56\cdot \:4\\\mathrm{Simplify}\\7y=224\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7y}{7}=\frac{224}{7}\\Simplify\\y=32[/tex]

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

[tex]3x - 7 = 8[/tex]

[tex]3x = 8+7[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Answer:

x=5

Step-by-step explanation:

Let's solve your equation step-by-step.

3x−7=8

Step 1: Add 7 to both sides.

3x−7+7=8+7

3x=15

Step 2: Divide both sides by 3.

3x/3=15/3

x=5

Answer:no it doesn’t vary

Step-by-step explanation:because if you count them up there is no possibility that they match

Answer:

F(2)=3

Step-by-step explanation:

The first term is -1.5= f(1).

So  F(1+1)=-2*f(1)= (-1.5)*(-2)=3

Answer:

(a) [tex]A_1[/tex] and [tex]A_2[/tex] are indeed mutually-exclusive.

(b) [tex]\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}[/tex], whereas [tex]\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}[/tex].

(c) [tex]\displaystyle P(B) = \frac{9}{100}[/tex].

(d) [tex]\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}[/tex], whereas [tex]P(A_1 \; |\; B) = \displaystyle \frac{4}{9}[/tex]

Step-by-step explanation:

[tex]P(A_1 \; \cap \; A_2) = 0[/tex] means that it is impossible for events [tex]A_1[/tex] and [tex]A_2[/tex] to happen at the same time. Therefore, event [tex]A_1[/tex] and [tex]A_2[/tex] are mutually-exclusive.

By the definition of conditional probability:

[tex]\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}[/tex].

Rearrange to obtain:

[tex]\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}[/tex].

Similarly:

[tex]\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}[/tex].

Note that:

[tex]\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}[/tex].

In other words, [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive. Since [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive and mutually-exclusive at the same time:

[tex]\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}[/tex].

By Bayes' Theorem:

[tex]\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}[/tex].

Similarly:

[tex]\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}[/tex].

Using probability concepts, along with conditional probability and Bayes Theorem, it is found that:

a) [tex]P(A1 \cap A2) = 0[/tex], thus yes, A1 and A2 are mutually exclusive.

b) The probabilities are: P(A1 ∩ B) = 0.05, P(A2 ∩ B) = 0.04.

c) The probability of event B is: P(B) = 0.09.

d) The probabilities are: P(A1|B) = 0.5555 and P(A2|B) = 0.4445.

-----------

Conditional Probability  

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]  

-----------

Bayes Theorem:  

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

-----------

Item a:

Item b:

Using conditional probability.

A1 and B:

[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]

[tex]0.25 = \frac{P(A1 \cap B)}{0.2}[/tex]

[tex]P(A1 \cap B) = 0.25(0.2) = 0.05[/tex]

A2 and B:

[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]

[tex]0.05 = \frac{P(A1 \cap B)}{0.8}[/tex]

[tex]P(A1 \cap B) = 0.8(0.05) = 0.04[/tex]

Item c:

P(B) is given by:

[tex]P(B) = P(A1 \cap B) + P(A2 \cap B) = 0.05 + 0.04 = 0.09[/tex]

Item d:

Applying Bayes Theorem

[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.25(0.2)}{0.09} = 0.5555[/tex]

[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.8(0.05)}{9} = 0.4445[/tex]

A similar problem is given at https://brainly.com/question/22428992

Answer:

122 miles per hour.

Step-by-step explanation:

Time:108 min ÷60 =1.8 hours

Speed = distance /time = 219/1.8 =122 miles per hour.

Hope this helps..

Answer:

No its 121.67 mph.

Step-by-step explanation:

Speed in miles per minute is 219/108 miles per minute

To convert to miles per hour we multiply by 60:

= 219 * 60 / 108

= 121.67 m p h.

Answer:

The easiest way to factor it is to use grouping.

Step-by-step explanation:

you look at only two terms at a time to see if any techniques become apparent.

The grouping factoring method should be used to factor a polynomial with four terms.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The simplest method to factor a polynomial with four or more parts is to use grouping. With this approach, you evaluate just two terms at once to determine whether any methods stand out.

Therefore, the grouping factoring method should be used to factor a polynomial with four terms.

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Answer:

1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies

2) Now let's consider any real number a no matter positive or negative we will have that:

[tex]a-a =0[/tex]

Or in the other case:

[tex]-a -(-a) =-a +a=0[/tex]

So then we can conclude that the expression is a general rule and is true

Step-by-step explanation:

For this case we can verify if the following expression is true or false:

The sum of x and it’s opposite is always zero?

If we want to proof this we need to show that for any number is true.

1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies

2) Now let's consider any real number a no matter positive or negative we will have that:

[tex]a-a =0[/tex]

Or in the other case:

[tex]-a -(-a) =-a +a=0[/tex]

So then we can conclude that the expression is a general rule and is true

Answer:

  C. F(x) = | x |

Step-by-step explanation:

The parent function has no adornments, shifts, multipliers, offsets, reflections, or anything else.

The absolute value of x is written |x|. That is the parent absolute value function.

  F(x) = |x|

Answer: C

Step-by-step explanation: