MATHEMATICS COLLEGE

76,80,88,95,100,101,? Which number comes next in this sequence?

Answers

Answer 1

Answer:

Answer:

112

Step-by-step explanation:

Difference between each 4,8,7,5,1

Add numbers next to each other in pairs = 12

So 12-1= 11 and

101+11=112

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Chris had a job walking dogs on the weekends. He earned $8.75 per dog. He walked 5 dogs a week for 7 weeks. How much money did Chris earn?

Answers

Answer:

Chris's total earning will be: $306.25

Step-by-step explanation:

Given:

Total number of dogs = d = 5

Number of weeks = w = 7

Cost for walking per dog = c = $8.75

First of all, we will calculate his per week cost of walking 5 dogs

Per week cost of walking 5 dogs = d*c = 8.75*5 = $43.75

Then for the cost of 7 weeks, the amount of one week will be multiplied by 7

Total earning will be:

$= 43.75*7 = 306.25$

Hence,

Chris's total earning will be: $306.25

Answer:

he should be making $306.25

Step-by-step explanation:

what i did was multiply his $8.75 a dog by 5 then multiply it by the 7 weeks

Determine whether the improper integral converges or diverges, and find the value of each that converges.∫^0_-[infinity] 5e^60x dx

Answers

Answer:

The improper integral converges.

$\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1)/(12)$

General Formulas and Concepts:
Calculus

Limit

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_(x \to c) x = c$

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = (x^(n + 1))/(n + 1) + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Method: U-Substitution

Improper Integral: $\displaystyle \int\limits^(\infty)_a {f(x)} \, dx = \lim_(b \to \infty) \int\limits^b_a {f(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx$

Step 2: Integrate Pt. 1

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = 5 \int\limits^0_(- \infty) {e^(60x)} \, dx$
[Integral] Rewrite [Improper Integral]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) 5 \int\limits^0_(a) {e^(60x)} \, dx$

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Set u: $\displaystyle u = 60x$
[u] Differentiate [Derivative Properties and Rules]: $\displaystyle du = 60 \ dx$
[Bounds] Swap: $\displaystyle \left \{ {{x = 0 \rightarrow u = 0} \atop {x = a \rightarrow u = 60a}} \right.$

Step 4: Integrate Pt. 3

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1)/(12) \int\limits^0_(a) {60e^(60x)} \, dx$
[Integral] Apply Integration Method [U-Substitution]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1)/(12) \int\limits^0_(60a) {e^(u)} \, du$
[Integral] Apply Exponential Integration: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1)/(12) e^u \bigg| \limits^0_(60a)$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1 - e^(60a))/(12)$
[Limit] Evaluate [Limit Rule - Variable Direct Substitution]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1 - e^(60(-\infty)))/(12)$
Rewrite: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1)/(12) - (1)/(12e^(60(\infty)))$
Simplify: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1)/(12)$

∴ the improper integral equals $\displaystyle \bold{(1)/(12)}$ and is convergent.

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Learn more about improper integrals: brainly.com/question/14413972

Learn more about calculus: brainly.com/question/23558817

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Topic: AP Calculus BC (Calculus I + II)

Unit: Integration

Answer:

$\int_(-\infty)^0 5 e^(60x) dx = (1)/(12)[e^0 -0]= (1)/(12)$

Step-by-step explanation:

Assuming this integral:

$\int_(-\infty)^0 5 e^(60x) dx$

We can do this as the first step:

$5 \int_(-\infty)^0 e^(60x) dx$

Now we can solve the integral and we got:

$5 (e^(60x))/(60) \Big|_(-\infty)^0$

$\int_(-\infty)^0 5 e^(60x) dx = (e^(60x))/(12)\Big|_(-\infty)^0 = (1)/(12) [e^(60*0) -e^(-\infty)]$

$\int_(-\infty)^0 5 e^(60x) dx = (1)/(12)[e^0 -0]= (1)/(12)$

So then we see that the integral on this case converges amd the values is 1/12 on this case.

State if the two triangles are congruent. If they are, state how you know.1) SSS
2) SAS
3) ASA
4) AAS
5) NOT CONGRUENT

Pic is up right answer = brainliest

Answers

The two triangles ΔABC and ΔCDA are congruent. Then the correct option is B.

What is a rectangle?

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The rectangle is ABCD is given below.

In triangles ΔABC and ΔCDA,

AB = CD (opposite sides)

BC = AD (opposite sides)

∠ABC = ∠ADC = 90°

The two triangles ΔABC and ΔCDA are congruent. Then the correct option is B.

More about the rectangle link is given below.

brainly.com/question/10046743

#SPJ2

Answer: Your answer is 2) SAS

Step-by-step explanation: Yes, there are congruent.

How many centimeters are equivalent
to 2.5 meters?

Answers

Answer:

250 centimeters

Step-by-step explanation:

............

in cm 2.5 meters are 250 cm

reason 2.5*100=250

Identify the number that is 9.5 units from 2 on a number line

Answers

There are two such numbers.

One of them is 2 + 9.5 = 11.5.

The other one is 2 - 9.5 = -7.5.

_____

If we consider "9.5 units from 2" to be 9.5 units in the positive direction, then the appropriate choice is 11.5.

$\boxed{\large{\bold{\blue{ANSWER~:) }}}}$

we have to find the number that is 9.5 units from 2 on a number line

Ithas2typesofnumber

such as:

2+9.5=11.5
2-9.5=-7.5

we can represented it on the number line

(See this attachment)

A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationshipbetween the given line segment and its image is true?
A The line segments are parallel, and the image is twice the length of the given line segment.
B. The line segments are parallel, and the image is one-half of the length of the given line segment.
C. The line segments are perpendicular, and the image is twice the length of the given line segment.
DD The line segments are perpendicular, and the image is one-half of the length of the given line segment.

Answers

9514 1404 393

Answer:

A The line segments are parallel, and the image is twice the length of the given line segment.

Step-by-step explanation:

Dilation by a factor of 2 means any measure of the image is 2 times the corresponding measure of the original.

Dilation does not change any orientations, so the image will have the same orientation with respect to the origin, axes, or any other line segments. That means the dilated segment is parallel to the original. (If the center of dilation is on the original line segment, the dilated segment will overlay the original segment. That is specifically not the case here.)

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