TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested

Answer:

  (b)  x + 6

Step-by-step explanation:

You want the rule for the x-coordinate when the transformation is a right shift of 6 units.

A point that is the image of a pre-image point with x-coordinate x will be 6 units farther right of the y-axis than the pre-image point.

The x-coordinate measures how far right of the y-axis a point is. When that distance increases by 6 units, the x-coordinate increases by 6 units:

  x ⇒ x+6 . . . . . . the x-coordinate transformation rule

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a) 22+35+33+18+16+12+28+18+17 is 199, and 199 divided by 10 is 19.9, so 19.9 is the mean.

b) if he gets 10 more home runs, then he has 209 divided by 11 which is 19

Answer:

A reasonable tip amount is roughly $12.44

Step-by-step explanation:

0.15 * 82.99 = 12.4485

$12.4485

Answer:

¹/₄ hr or 0.25 hrs

⁷/₆ hr or 70 mins

He will make it in time (justification below)

4.

a. False

b. True

c. False

Step-by-step explanation:

The questions are all in relation to the equation:

speed (km/hr) = distance (km)/time (hr)

It may be worth learning about how formula triangles work because I think you would find them helpful, there are videos online on this

The first question is asking about times;

Rearranging the equation/formula above, time = distance/speed;

So, we just plug in the information for each distance travelled;

The first 30 km is covered at 120 km/hr;

So, the time taken will be:

t = ³⁰/₁₂₀

This simplifies to:

t = ¹/₄ = 0.25

So, it will take ¹/₄ hr or 0.25 hrs to cover 30 km at 120 km/hr;

¹/₄ hr is the same as 15 mins

The next 56 km is covered at 48 km/hr;

So:

t = ⁵⁶/₄₈

This simplifies to:

t = ⁷/₆

So, it will take ⁷/₆ hr or 70 mins

The second question requires us to know the time taken to cover 16 km at 100 km/hr;

t = ¹⁶/₁₀₀

This simplifies to:

t = ⁴/₂₅ = 0.16

So, ⁴/₂₅ hr or 9.6 mins

If he has 15 mins to make it to school and we've just calculated it will taken 9.6 mins, then he will make it in time

4.

a.

False

Jason runs 5 km in 30 mins, which means he could run 10 km in 60 mins;

Donna runs 9 km in 60 mins, so Jason runs at a faster speed since he would cover 10 km in 60 mins

b.

True

Rachel covers 10 km in 10 mins;

Speed will be:

10/10 = 1

So, her speed is 1 km/min

An hour is 60 mins so, her speed in km/hr will be:

60 × 1 = 60

60 km/hr

This is greater than the limit 50 km/hr

c.

False

The 2 runners run the same track, this means they run the same distance;

If James takes longer, then this is because he is running slower or, in other words, Paula is running faster

d.

Can't see the full question

Answer:

e + 2/ 5  = 4

Hope this helps, and be sure to report the answer that had a link

Step-by-step explanation:

Answer:

The third side of the triangle must have a length between 23 yd and 41 yd.

Step-by-step explanation:

Triangle Inequality Theorem

Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:

x + y > z

x + z > y

y + z > x

Combining the above inequalities, and provided y>z, the third size must satisfy:

y - z < x < y + z

We have to side lengths: y=32 yd and z = 9 yd, thus the range of possible values for the third side x is:

32 - 9 < x < 32 + 9

23 < x < 41

The third side of the triangle must have a length between 23 yd and 41 yd.

Answer:

it is equal to 0

Answer:

For the table- k=2

For the graph- no constant of proportionality

For the coordinates- k=3/2

Step-by-step explanation:

I got it all correct.

Answer:

T = 67.5

V = 22.5

Step-by-step explanation:

The Sum of triangle angles = 180

180 = W + T + V

180 = 90 + 3X + X

X = 22.5

Answer:

5xsquared+x+5

Step-by-step explanation:

first combine x squared with 4x squared and you will get 5xsquared.

next combine 6x and -5x and you will get 1x or just simply x. Finally combine 3 and 2 (3+2) = 5.

Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer: A

Step-by-step explanation: c shifts the graph up or down.

Answer:

25

Step-by-step explanation:

Ratios:

\(\frac{36}{100} =\frac{9}{x} \\\\36x=900\\x=25\)

Double check:

25(0.36) = 9

You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.

Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.

For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.

Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.

The correct answer is C.

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9514 1404 393

Answer:

  row 13

Step-by-step explanation:

The sum of row n is 2^n, so the row number with a particular sum is ...

  2^n = sum

  n·log(2) = log(sum)

  n = log(sum)/log(2)

The row with sum 8192 is ...

  n = log(8192)/log(2) = 13

The row of Pascal's triangle that has a sum of 8192 is row 13.

Answer:

5b+4

Step-by-step explanation:

1/2(20b-10b+8)

By distribution, (10b-5b+4)= 5b+4

Answer:

False

Step-by-step explanation:

Although it is true that y=-2 is a horizontal line, it does not have an undefined slope. Because it is a horizontal line, it has a slope of 0.

Answer:

13.5

Step-by-step explanation:

total boxes of granola is = 3 + 2 + 1

                                         =  6 boxes

6 boxes = 57 bars

1 box  =  57 / 6

1 box  = 9.5 + 3

           = 13.5 (ANS)

i hope my ans is correct if not i apologise.

No, we do not have enough information to find out the percentage of Americans who either do not follow football or do not follow basketball. We would need to know the percentage of Americans who do follow both sports.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 out of 100 questions correctly on a test, you would have received a 75%.

The percent sign (%), which denotes a division by 100, is used. Therefore, 25% translates to 25/100, or 1/4. Dividing by 100 will change a percentage to a decimal. Therefore, 25% is equal to 25/100, or 0.25. A decimal can be multiplied by 100 to become a percentage (just move the decimal point 2 places to the right)

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Answer:

There are 0

Step-by-step explanation:

Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true

Answer:

A 0

Step-by-step explanation:

There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.

If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.

Answer: 8

Step-by-step explanation:

420/12 is 35

540/20 is 27

35-27=8

Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system

x⃗' (t) = A x⃗ ( t )

the possible values of c₁ is 1 and c₂ is 2 .

So, the correct option is option(a) and (e).

We have given that A is 2 × 2 diagonalizable matrix and x⃗ (t) = ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) is a solution of system, x⃗ '(t) = A x⃗(ᵗ) .

A Solution of system always satisfied the equation of system.

Now, Differenating x⃗ (t) wih respect to t we get, x⃗' (t)=( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)

So, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)= A ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) where A is diagonalizable and A = [a 0 0 b].

Then, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ) = ( 3aeᵗ + aeᶜ₁t , 3be²ᵗ + b eᶜ₂ᵗ)

equating the coefficients on both sides we get, 3eᵗ + c₁ eᶜ₁t = 3aeᵗ + aeᶜ₁t 6e²ᵗ + c₂ eᶜ₂ᵗ = 3be²ᵗ + b eᶜ₂ᵗ

after equating the corresponding equations , 3 = 3a and c₁ = a and 6 = 3b and c₂ = b after solving all we get a = 1 and b = 2 which implies c₁ = 1 and c₂ = 2. Hence, the possible values are c₁ = 1 and c₂ = 2.

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Complete question:

Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system x⃗ (t) = A x⃗

then check all the possible values of c₁ and c₂ and below.

(a) c₁ = 1

(b) c₁ = 3

(c) c₁ = 2

d) c₂ = 1

(e)c₂ =2

(f) c₂ = 3

Answer:5

Step-by-step explanation:

5098

True 6. If the obtained sample data (test statistic value) falls inside the critical region, it provides support for the researcher's hypothesis.

True 7.  When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

True 8. If the obtained sample data (test statistic value) is not in the critical region, it means that the observed result is likely to have occurred by chance under the assumption of the null hypothesis. hypothesis.

True 9. Failing to reject the null hypothesis means that the data do not provide sufficient evidence to conclude that the treatment or independent variable had a significant effect on the dependent variable.

True 10.  Whenever the statistical decision is to fail to reject the null hypothesis, there is a possibility of making a Type I error.

6. The critical region is determined based on the desired level of significance and contains the extreme values that would lead to rejecting the null hypothesis.

7. When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

8. In this case, we do not have sufficient evidence to reject the null hypothesis, and the correct statistical decision is to "fail to reject" the null

9. It does not necessarily mean that the treatment had no effect, but rather that the evidence in the sample is not strong enough to support such a claim.

10. Type I error refers to rejecting the null hypothesis when it is actually true. The probability of committing a Type I error is denoted by the significance level (usually denoted as alpha) and is predetermined before conducting the statistical test.

In summary, the statements are all true. The critical region plays a crucial role in hypothesis testing, and the decisions made based on the test statistic falling inside or outside the critical region determine whether the null hypothesis is rejected or failed to be rejected.

Failing to reject the null hypothesis does not provide sufficient evidence to support the researcher's hypothesis and there is always a possibility of making a Type I error when conducting hypothesis tests.

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Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

Answer:

x = -1

Step-by-step explanation:

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer: 5/3a + 4/2b

Step-by-step explanation:

\(\dfrac{4}{3} a-\dfrac{1}{2} b+\dfrac{1}{3} a+\dfrac{5}{2} b\)

Rearrange:

\(\dfrac{4}{3} a+\dfrac{1}{3} a-\dfrac{1}{2} b+\dfrac{5}{2} b\)

Combine Like Terms:

\(\dfrac{4}{3} a+\dfrac{1}{3} a=\dfrac{5}{3} a\\-\dfrac{1}{2}b+\dfrac{5}{2} b=\dfrac{4}{2} b\)

\(\fbox{$\dfrac{5}{3}$a + $\dfrac{4}{2}$b}\)