A caterpillar crawling in a straight line across a coordinate plane starts at point (-3, -4) and ends at point (25, 38). Counting the start point and end point, how many points with integer coordinates does the caterpillar touch?

Answer:

1. x=17

  y= 7 1/3

2. x= 6 2/3

   y=1.7

Step-by-step explanation:

4x=68 because it is isosceles triangle

x=17

y+1/2= 7 5/6

y= 7 1/3

Answer:$15.18

Step-by-step explanation:

The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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As several differences are there between them and is differentiated below.

A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.

Let a sequence's terms be a1, a2, a3,..., an,..., etc.

The term's position is indicated by the subscripts. That implies,

Initial phrase = a1

term two = a2

term three Equals a3

….

The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.

Geometric Sequence:

Arithmetic Sequence:

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9514 1404 393

Answer:

  $313.37

Step-by-step explanation:

The compound interest formula is used to find that value.

  A = P(1 +r/12)^(12t)

P compounded monthly at annual rate r for t years.

  A = $200(1 +0.05/12)^(12·9) ≈ $313.37

Answer:

The null and alternative hypothesis can be written as:

\(H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0\)

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

This claim will be reflected in the alternnative hypothesis, that will state that the population proportion 1 (18 to 34) is significantly smaller than the population proportion 2 (35 to 49).

On the contrary, the null hypothesis will state that the population proportion 1 is ot significantly smaller than the population proportion 2.

Then, the null and alternative hypothesis can be written as:

\(H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0\)

The significance level is assumed to be 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.63.

\(p_1=X_1/n_1=126/200=0.63\)

The sample 2, of size n2=175 has a proportion of p2=0.68.

\(p_2=X_2/n_2=119/175=0.68\)

The difference between proportions is (p1-p2)=-0.05.

\(p_d=p_1-p_2=0.63-0.68=-0.05\)

The pooled proportion, needed to calculate the standard error, is:

\(p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{126+119}{200+175}=\dfrac{245}{375}=0.653\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.653*0.347}{200}+\dfrac{0.653*0.347}{175}}\\\\\\s_{p1-p2}=\sqrt{0.001132+0.001294}=\sqrt{0.002427}=0.049\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.05-0}{0.049}=\dfrac{-0.05}{0.049}=-1.01\)

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

\(\text{P-value}=P(z<-1.01)=0.1554\)

As the P-value (0.1554) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

Which negative angle is equivalent to an 85° angle?

A. An angle measuring -95°

B. An angle measuring -275°

D. An angle measuring -265°

-KeonLee

I hope it help

#Carry on learning

An angle measuring -275°

*view photo*

Answer:

18.67

Step-by-step explanation:

my calculate ratio results

Answer:

  1982.0 ft³

Step-by-step explanation:

The composite figure can be decomposed into a cube and a square pyramid. The volume is the sum of the volumes of these.

__

The square base of the pyramid is 12 ft on each side, so the diagonal of the base is 12√2 feet. (The diagonal of a square is √2 times the side length.) Then the distance from a corner to the center of the base is half that, or 6√2 feet.

That distance and the height of the pyramid form a right triangle whose hypotenuse is the given 10 ft measure of the length of the edge of a face of the pyramid. Then the height can be found using the Pythagorean theorem:

  h² +(6√2)² = 10²

  h² = 100 -72 = 28

  h = 2√7 ≈ 5.291503 . . . ft

The volume of the pyramid is ...

  V = 1/3Bh = 1/3s²h

  V = 1/3(12 ft)²(5.2910503 ft) ≈ 253.992 ft³

__

The volume of a cube is given by ...

  V = s³

  V = (12 ft)³ = 1728 ft³

__

The total volume of the figure is the sum of the pyramid volume and the cube volume:

  total volume = 253.992 ft³ +1728 ft³ = 1981.992 ft³

The volume of the figure is about 1982.0 ft³.

_____

Additional comment

Your figure for the volume seems to assume the height of the pyramid is 8 feet. That length is the slant height of one face of the pyramid. It would be the hypotenuse of a right triangle whose other legs are 6 ft and the height of the pyramid. Then we would have ...

  h² +6² = 8²

  h² = 64 -36 = 28 . . . . as above

The pyramid height is the perpendicular distance from the plane of the base to the peak. It is measured through the middle of the volume, not along one face.

Answer:

Pour calculer la moyenne, nous devons multiplier chaque valeur par sa fréquence, additionner tous les produits, puis diviser par la fréquence totale.

Le calcul ressemblerait à ceci :

(7 * 7) + (8 * 1) + (9 * 1) + (10 * 1) + (11 * 1) + (12 * 3) + (13 * 2) + (14 * 1) + (15 * 1) + (16 * 1) + (18 * 1)

= 49 + 8 + 9 + 10 + 11 + 36 + 26 + 14 + 15 + 16 + 18

= 238

Fréquence totale = 7 + 1 + 1 + 1 + 1 + 3 + 2 + 1 + 1 + 1 + 1 = 21

Moyenne = 238/21 = 11,333

La moyenne de la série est de 11,3333.

Answer:

Step-by-step explanation:

You want the solution to right triangle RST with RS = 15, R = 72°, T = 90°.

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse   ⇒   r = 15·sin(72°) ≈ 14.3

  Cos = Adjacent/Hypotenuse   ⇒   s = 15·cos(72°) ≈ 4.6

The acute angles in a right triangle are complementary, so ...

  S = 90° -R = 90° -72° = 18°

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

What is the Linear equation?

An algebraic equation with only a constant and a first-order (linear) term is said to be linear if it has the formula y = mx + b, where m is the slope and b is the y-intercept. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

y = mx + c

where m denotes the slope.

The y-intercept is represented by the constant c. (Where x is zero)

In our instance, y-intercept equals 60.

The line's equation will therefore be:

y = mx + 60

y = mx + 60

There are given the line's coordinates (4, 90). These considerations will thus satisfy the equation.

90 = 4*m + 60

4.m = 30 m = 7.5 m = 7.5 y = 7.5x + 60 y = 7.5 * 6 + 60 y = 45 + 60 y = 105 is

y = 7.5x + 60.

If Adam's study for 6 hours then his score would be

y = 7.5x + 60.

y = 7.5(6) + 60

y = 105

Hence,

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

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Answer:

4x - 3 - 2x + 5 = 6 - 3x + 2 + 5x

2x + 2 = 2x + 8

2 ≠ 8, so this equation has no solutions.

Answer:

No solution

Step-by-step explanation:

Given:

\(4x-3-2x+5=6-3x+2+5x\)

rearrange terms so like terms are together

\(4x-2x-3+5=6+2-3x+5x\)

combine like terms

\(2x+2=8+2x\)

subtract 2x to both sides

\(2\neq 8\)

2 doesn't equal 8, meaning that there are 0 solutions to this problem.

Hope this helps! :)

Heather's account balance will be approximately $1,340.55 after 7 years if the interest is compounded 6 times each year.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the account balance after a certain amount of time

P is the principal or initial amount invested

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

Given tha data in the question;

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 rate per year.

Substituting these values into the formula solve for accrued amount, we get:

A = P(1 + r/n)^(nt)

A = 1,050(1 + 0.035/6)^(6 × 7)

A = 1,050(1 + 0.005833333333333)⁴²

A = 1,050(1.005833333333333333)⁴²

A = $1,340.55

Therefore, the accrued amount is $1,340.55.

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Answer:

\(\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}\)

Step-by-step explanation:

We can use Heron’s formula to determine the area of a triangle when three side lengths of a triangle are given.

\(s=\frac{a+b+c}{2}\)

\(s : \mathrm{semi \: perimeter}\)

\(A=\sqrt{s(s-a)(s-b)(s-c)}\)

\(A : \mathrm{area}\)

Answer:

Heron's formula gives the area of a triangle when the length of all three sides are known. Use Heron's formula to find the area of triangle ABC, if AB=3,BC=2,CA=4 . Substitute S into the formula . Round answer to nearest tenth.

Step-by-step explanation:

When performing a transformation to a point on the coordinate system, if the coordinates are multiplied by a constant k the resulting transformation will be a dilation.

If k > 1 → the resulting dilation is an enlargment

If k < 1 →the resulting dilation is a reduction

For the given rule

(1.5x,1.5y)

The constant is k=1.5, the resulting transformation is an enlargement.

To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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The solutions are: x = ln(2) for 2eˣ = 4,  x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.

To solve these equations using natural logarithm, we can use the following rules:

Using these rules, we can solve the given equations as follows:

2eˣ = 4

Divide both sides by 2 to get

eˣ = 2.

Take the natural logarithm of both sides to get

ln(eˣ) = ln(2).

Using rule 1 above, we can simplify ln(eˣ) to x, and we get

x = ln(2).

e⁴ˣ = 25

4x = ln(25).

Divide both sides by 4 to get

x = ln(25)/4.

eˣ = 72

Take the natural logarithm of both sides to get

x = ln(72).

e³ˣ = 124

Take the natural logarithm of both sides to get

3x = ln(124).

Divide both sides by 3 to get

x = ln(124)/3.

For the second set of equations, we use the same rule as above

So, we have

ln(x - 3) = 2

x - 3 = e²

x = e² + 3.

x ≈ 10.389.

Therefore, the solution is x ≈ 10.389.

ln(2t) = 4

2t = e⁴

t = 0.5 * e⁴

t ≈ 27.299.

Therefore, the solution is t ≈ 27.299.

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Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

Answer:

\( - 8(45) + 482 = - 360 + 482 = 122\)

A linear function must satisfy the condition that the slope between any two points must remain the same.

Use this fact to find pairs of points which do not satisfy that condition. That will tell you which options are not linear functions.

A)

The slope of points (-2,0) and (1,-3) is -1 while the slope of points (1,-3) to (3,-6) is -3/2. Then, this is not a linear function.

B)

The slope of every pair of numbers here is 2. Then, this set represents a linear function.

C)

The slope of points (-7,-7) and (-3,-4) is 3/4 while the slope of points (-3,-4) and (0,-1) is -1. Then, this is not a linear function.

D)

The slope of points (3,3) and (5,4) is 1/2 while the slope of (5,4) and (7,6) is 1. Then, this is not a linear function.

Therefore, the answer is:

The probability of drawing a penny dated 1977 is 0.24 or 24%.

Probability is a branch of mathematics that deals with the study of random events. It is used to measure the likelihood or chance of a particular event occurring.

Probability is expressed as a fraction or a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

The probability of drawing a penny dated 1977 can be found by dividing the number of pennies dated 1977 by the total number of pennies.

Here we have

Total number of pennies = 50

Number of pennies dated 1977 = 12

Probability of drawing a penny dated 1977

= Number of pennies dated 1977 / Total number of pennies

= 12 / 50

= 0.24

Therefore,

The probability of drawing a penny dated 1977 is 0.24 or 24%.

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Bob would take 5 hours to mow the law by himself.

Let us consider, the area of the lawn to be mowed to be x inch².

It is given that the law can be mowed by Abe alone in 3 hours.

We know that,

Rate of work = Work/Time

⇒ rate of work of Abe = area to be mowed(work)/time taken

                                     = (x/3) inch²/hour

Now,

Abe has been working alone for 1/3 hour

⇒work done by Abe alone = rate of work of Abe x time

                                             = (x/3) inch²/hour x 1/3 hour

                                             = x/9 inch²

Remaining work = x - x/9 = 8x/9 inch²

Let, the rate of work of Bob be y inch²/hour.

It is given that the time taken by Abe and Bob to complete the remaining work together is  1 and 2/3 hours, i.e, 5/3 hours.

Therefore,

The rate of work of Abe and Bob when working together

= work ÷ time

=(8x/9) ÷ (5/3)

=8x/15 inch²/hour

⇒ Rate of work of Abe + Rate of work of Bob = 8x/15

⇒ x/3 + y = 8x/15

⇒ y = (8x/15) - (x/3)

⇒ y = 3x/15 = x/5 inch²/hour

Thus, the time taken by Bob to mow the law by himself

= work ÷ rate of work

= x inch² ÷ (x/5) inch²/hour

= 5 hours

So, it would take 5 hours for Bob to mow the lawn alone.

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Answer:

I'm pretty sure the answer is 575 :D

Step-by-step explanation:

1,000 minus 425 is 575. have a good day!

Answer:

138 grams of zinc

Step-by-step explanation:

Zinc : copper = 3 : 19

Let amount of zinc = 138 grams

3 : 19 :: x : 874

Product of means  = product of extremes

19 * x = 3 * 874

      x = \(\frac{3*874}{19}\)

      x = 3 * 46

Zinc = 138 grams

\(\underline{\underline{\sf \bigstar \qquad Solution \qquad \: \bigstar}} \\ \)

Let weight of copper be 3x and weight of zinc be 19x.

☯ \(\underline{\boldsymbol{According\: to \:the\: Question\:now :}} \\\)

\(:\implies \textsf {Total weight = weight of copper + weight of zinc} \\ \\ \\ \)

\(:\implies \textsf {Total weight = 3x +19x} \\ \\ \\ \)

\(:\implies \underline{ \boxed{ \textsf {Total weight = 22x}}} \\ \\ \\ \)

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━

\(\dashrightarrow\:\:\textsf{ Weight of chemical = weight of zinc + weight of copper} \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x = 3x + 19x \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x = 3x + 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x - 3x = 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 19x = 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf x = \dfrac{874}{19} \\ \\ \\ \)

\(\dashrightarrow \: \: \underline{\boxed{ \sf x = 46}} \\ \\ \\\)

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

\(\bigstar\:\underline{\frak{Finding \: the \: weight \: of \: the \: zinc \: in \: a \: chemical : }}\)

\(\longrightarrow\:\:\sf weight \: of \: zinc = 3x \\ \\ \\ \)

\(\longrightarrow\:\:\sf weight \: of \: zinc = 3 \times 46 \\ \\ \\ \)

\(\longrightarrow\:\: \underline{ \boxed{\sf weight \: of \: zinc =138 \: grams}} \\ \\ \\ \)

\(\therefore\:\underline{\textsf{The chemical contains \textbf{138 grams}} \textsf{ of zinc}}. \\ \)