Once a week you babysit your neighbor’s toddler after school, usually going to a local playground. You notice that each swing on the swing set takes nearly the same amount of time, about 2.7 seconds. Use the pendulum formula below to find out how long the swing is. Round your answer to the tenths place. A.37 feetB.5.4 feetC.1.8 feetD.5.9 feet

The simplest form of inequality would be x < -1 (or) \(\frac{3}{5}\leq x < 1\).

What is rational equality?

A rational inequality is one that contains a rational expression, where the rational expression is a polynomial ratio. A rational expression is one of the following:

R(x) / Q(x), where R(x) and Q(x) are polynomials and Q(x) is not zero.

The given expression is \((\frac{x-1}{x-1})\frac{x+5}{x+1} - \frac{x-2}{x-1}(\frac{x+1}{x+1})\leq 0\)

Now solving the above equality, we get

                          \(\frac{(x+5)(x-1)}{(x-1)^2} - \frac{(x-2)(x+1)}{(x-1)^2}\leq 0\\\frac{(5x-3)}{(x-1)^2}\leq 0\)

              Let's find the critical point, we get

                         \(\frac{5x-3}{x^2-1}= 0\\\\5x-3=0\\x=\frac{3}{5}\)

              x = 1 (or) x = −1 (Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

                              x < −1 (Works in original inequality)

                            \(-1 < x\leq \frac{3}{5}\)  (Doesn't work in original inequality)

                              \(\frac{3}{5}\leq x < 1\)   (Works in original inequality)

                          x > 1 (Doesn't work in original inequality)

Hence, The simplest form of inequality would be x < -1 (or) \(\frac{3}{5}\leq x < 1\).

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Answer:

There are a total of 25 marbles in the bag.

The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.

Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.

The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.

To find the probability of both events occurring together, we multiply their individual probabilities:

8/25 x 1/8 = 1/25

Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.

Answer:

P(X is less than 348) = 0.2148

Step-by-step explanation:

Given that:

Sample proportion (p) = 0.3

Sample size = 1200

Let X be the random variable that obeys a binomial distribution. Then;

\(X \sim Bin(n = 1200,p =0.3)\)

The Binomial can be approximated to normal with:

\(\mu = np = 1200 \times 0.3 \\ \\ \mu= 360\)

\(\sigma = \sqrt{np(1-p) } \\ \\ \sigma = \sqrt{1200 \times (0.3)(1-0.3) } \\ \\ \sigma = 15.875\)

To find:

P(X< 348)

So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 348 lies between 347.5 and 348.5

Normal distribution:

x = 347.5, \(\mu\) = 360, \(\sigma\) = 15.875

Using the z test statistics;

\(z = \dfrac{x - \mu}{\sigma}\)

\(z = \dfrac{347.5 - 360}{15.875}\)

\(z = \dfrac{-12.50}{15.875}\)

z = -0.7874

z ≅ - 0.79

The p-value for P(X<347.5) = P(Z < -0.79)

From the z tables;

P(X<347.5) = 0.2148

Thus;

P(X is less than 348) = 0.2148

Answer:

15 ways

Step-by-step explanation:

girl 1 and boy 1

girl 2 and boy 1

girl 3 and boy1

girl 1 and boy 2

girl2 and boy 2

girl 3 and boy 2

girl 1 and boy 3

girl 2 and boy 3

girl 3 and boy 3

girl 1 and boy 4

girl 2 and boy 4

girl 3 and boy 4

girl 1 and boy 5

girl 2 and boy 5

girl 3 and boy 5

Answer: 4.5/5 = .9 * 60 = 54, so the answer is 54 minutes.

There are 10 and 26 candy bars of each size did he buy.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Diego brought 16 candy bars $25.

And, large candy bars cost $1.25 and regular candy bars cost $0.75.

Now, Let number of large candy bars = x

And, Number of regular candy bars = y

Here, Diego brought 16 candy bars.

Hence, We get;

⇒ x + y = 16  .. (i)

And, large candy bars cost $1.25 and regular candy bars cost $0.75.

Hence, We get;

⇒ 1.25x + 0.75y = 25  .. (ii)

Multiply by 1.25 in (i) and subtract from (ii),  we get;

⇒ 1.25y - 0.75y = 20 - 25

⇒ 0.5y = - 5

⇒ y = - 10

And, from (i);

⇒ x + y = 16

⇒ x - 10 = 16

⇒ x = 26

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Answer:

80.

Step-by-step explanation:

Answer:

-3x+1y=-1

or

3x-1y=1

or

by multiplying with 1/3 the first equation we get

-1x+1/3y=-1/3

or from second equation

1x-1/3y=1/3

Step-by-step explanation:

y-y1=m(x-x1)

y1=-7

x1=-2

m=3

so

y-(-7)=3(x-(-2))

y+7=3(x+2)

y+7=3x+6

-3x+y=6-7

-3x+ 1y= -1

Answer:

63.63 seconds, or round up if you need to?

Step-by-step explanation:

Answer:

In decimal form:

-0.875

Step-by-step explanation:

-7 divided by 8 = -0.875

Answer:

dw

Step-by-step explanation:

The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.

What is a congruent triangle?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The triangles are congruent by SAS congruency because

AC = CD (Given)

∠ACB = ∠DCE ( Vertically opposite angles)

BC = CE  (Given)

Thus, Triangle ABC ≅ Triangle DEC

Since, the triangles are congruent, therefore

⇒AC = CD

⇒4y-6 = 2x+6   ...(1)

Also, BC = CE

⇒3y+1 = 4x

⇒(3y+1)/4 = x    ...(2)

Now, substituting the value of x in (1), we get,

⇒4y-6 = 2(3y+1)/4+(6)

⇒4y-6 = (6y+2 +24)/4

⇒16y-24 = 6y+2 +24

⇒10y = 50

⇒y = 5

Now putting the value of y in (2), we get

⇒(3(2)+1)/4 = x

⇒7/4 = x

⇒ x = 1.75

Hence, the value of x is 1.75 and y is 5.

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Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

the answer is 4/5 this is know to be hard

Answer:

628 ft^2

Step-by-step explanation:

area of outer circle - area of inner circle

(15^2 *pi) - (5^2 *pi) =200 pi= 628.3185

To solve this problem we have to use Pythagorean's Theorem because we have a right triangle.

Remember that the theorem states that the squared hypotenuse is equivalent to the sum of the squared legs. Let's use it, the hypotenuse is 21 centimeters, one leg is 9 centimeters.

Where x is the missing leg. Let's solve for x.

Step-by-step explanation:

I just answered that. how often did you put that in ?

Answer:

Hello your question has some missing parts attached is the missing part

answer : slightly skewed to the right ( B )

Step-by-step explanation:

From the attached histogram related to the question above, it can be seen that the the right tail is longer than the left tail and this can help us draw the conclusion that the overall shape of the distribution is slightly skewed to the right

the value of 4% as a fraction is 1/25

4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.

Answer:

-12

Step-by-step explanation:

Answer:

let the unknown number be 'x'

x + (-12) = -24

x = -24+12

x = -12

Answer:

(0, -6) is the y-intercept.

Answer

B and C are true for sure but i am not sure about A or C.... i think it is C

Step-by-step explanation:

what is the rule for

8 units to the left, 2 units up

the rule is

the rule 6 units to the right , 4 units down

the rule is

Remember that

if the translation is at right is x+

if the translation is at left is x-

if the translation is up y+

if the translation is down is y-

The rule for the reflection across the x-axis is equal to

Find the coordinates of triangle JKL

looking at the graph

J(-4,2)

K(2,5)

L(8,4)

Apply the rule

J(-4,2) ------- J'(-4,-2)

K(2,5) -------- K'(2,-5)

L(8,4) -------> L(8,-4)

Part c

Triangle JKL and triangle J'K'L' are congruent

An invalid speculation is a sort of measurable theory that suggests that no factual importance exists in a bunch of offered viewpoints.

Speculation testing is utilized to evaluate the validity of a speculation by utilizing test information. It is represented as H0, and it is sometimes referred to as the "null."

Give the null hypotheses a name.

Negative hypothesis:

H. There is no correlation between gender and election participation.

Other possibilities:

H: Gender and participation in the most recent election are linked.

Rule of rejection:

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The quadratic equation from the given root is 4x² - 41x + 45 = 0

From the question, we have the following parameters that can be used in our computation:

Roots = 5/x and 4

The equation of the function can be calculated as

(x - root) * (x - root) = 0

using the above as a guide, we have the following:

(x - 5/4) * (x - 9) = 0

When expanded, we have

(4x - 5)(x - 9)/4 = 0

This gives

4x² - 5x - 36x + 45 = 4 * 0

So, we have

4x² - 41x + 45 = 0

Hence, the quadratic equation from the given root is 4x² - 41x + 45 = 0

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer:

Step-by-step explanation:

The points are plotted and the figure is a parallelogram with base and height both of 3 units long.

The area is:

The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.

Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.

According to the given information:

The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.

The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.

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