Is a parallelogram but not a rectangle

Answer:

a = 8 (to nearest whole number)

Step-by-step explanation:

Given:

m<B = 36°

m<C = 104°

c = 12

Required:

a

SOLUTION:

✔️First find m<A:

m<A = 180 - (104 + 36)

m<A = 40°

✔️Find a using Sine Rule:

Thus:

\( \frac{a}{sin(A)} = \frac{c}{sin(C)} \)

Plug in the values

\( \frac{a}{sin(40)} = \frac{12}{sin(104)} \)

Multiply both sides by sin(40)

\( \frac{a}{sin(40)} * sin(40) = \frac{12}{sin(104)} * sin(40) \)

\( a = \frac{12*sin(40)}{sin(104)} \)

\( a = 8 \) (nearest whole number)

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

for such more question on common difference

https://brainly.com/question/25731911

#SPJ8

Answer:

subtract 40 from both sides

Answer:

You subtract 40 which will equal -6 and now you divide  -6/4n and the answer is n=-1.5

Step-by-step explanation:

Answer:

theres no picture so how will we know

Step-by-step explanation:

post the picture first

Answer:

56cm2

Step-by-step explanation:

1÷3×4×6×7

=56cm2

The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.

Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

LEt suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

The dot plot is skewed to the right due to majority of the data occur to the right of the dot plot.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. Outliers usually occur with a frequency of one.

For Class A the dots are spread out more.

For Class B, the dots are more grouped together.

Here, Looking at the dot plot, it can be seen that the numbers that range from 16 to 21 have only one dot.

The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.

To learn more about outliers, please check: brainly.com/question/27197311

SPJ2

The volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x⁴ and y=125x is 138438\(\pi\).

Let,

f(x) = 125x

g(x) = x⁴

Intersection points will be,

x⁴ = 125x

x = 0 , 3.3437

Volume V = \(\pi\)\(\int\limits^{3.34}_0{(125x)^{2} - x^8 } \, dx\)

=\(\pi\)\(\int\limits^{3.34}_0 {15625x^2-x^8} \, dx\)

=\(\pi\)[15625x³/3 - x⁹/9]₀³

=\(\pi\)[140625 - 2187]

= 138438\(\pi\)

The volume of the solid formed by rotating the region inside the first quadrant enclosed by two curves can be found using the method of cylindrical shells. This method involves cutting the solid into thin cylindrical shells and finding the volume of each shell. The sum of the volumes of the shells is equal to the volume of the solid.

To learn more about volume of the solid click on,

https://brainly.com/question/22807624

#SPJ4

Answer:

\(\frac{1}{9^{8}}\)

Step-by-step explanation:

When multiplying two numbers with exponents with the same base, you simply add the two exponents together, even if they're negative:

\(9^{-5}*9^{-3} =9^{-8}\)

When a number has a negative exponent (\(x^{-2}\)) it means that the number is equal to 1/that number (\(\frac{1}{x^{2}}\))

\(9^{-8}=\frac{1}{9^{8}}\)

Answer:

 1.5

Explanation:

Given that:

While solving this problem, the above following is not required to use.

\(\rightarrow \sf log_b ([b^3])^{1/2}\)

apply log rule

\(\rightarrow \sf \dfrac{1}{2}\log _b\left(b^3\right)\)

\(\boxed{\sf \log _b\left(b^3\right)=3}\)

\(\rightarrow \sf \dfrac{1}{2}(3)\)

distribute

\(\rightarrow \sf \dfrac{3}{2} \quad or \quad 1.5\)

Answer:

B) 0.0069

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\(\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846\)

Find the probability that their mean rebuild time exceeds 9.1 hours.

This is 1 subtracted by the pvalue of Z when X = 9.1. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{9.1 - 8.4}{0.2846}\)

\(Z = 2.46\)

\(Z = 2.46\) has a pvalue of 0.9931

1 - 0.9931 = 0.0069

So the answer is B.

Dave and Frank are both right.

The correct answer would be Frank because 12 is less than 15.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that Frank ate 12 pieces of pizza and Dave ate 15 pieces. “I ate 1/4 more,” said Dave. “I ate 1/5 less,” said Frank.

Therefore, If Dave ate ¼ more than Frank, we would need to divide the denominator by the amount of pizzas,

Thus, if 12÷4 is 3 he ate three more pizzas than Frank.

If we do the same for Frank, ⅕

15÷5=3

Hence, the correct answer would be Frank because 12 is less than 15.

Learn more about multiplications;

https://brainly.com/question/14059007

#SPJ2

Answer:

x = -8

Step-by-step explanation:

\(\frac{3}{7} x + 5 = \frac{-4}{7} x - 3\\5 = -1x-3\\8 = -1x\\-8 = x\)

Answer:

The percent would be 10 Im guessing

Step-by-step explanation:

Hope this helped :)

Answer:

Correct me if I'm wrong but I'm sure it's -12

Step-by-step explanation:

34+30= 64

64-76= -12

\(yx=5\)

Explanation:

If \(y\) varies inversely as \(x\) then

         \(y\times x=k\) for some constant \(k\)

Since \(y = \frac{1}{8}\) when \(x=40\)

          \(\huge \text(\dfrac{1}{8}\huge \text)\times(40)=k\)

          \(\longrightarrow k=5\)

Answer:

(a) Let X be the number of boxes that do not have any balls. We can calculate the probability that a particular box is empty, which is (1-p)^10, where p is the probability that a ball is put into that box. The expected number of boxes that are empty is then:

E(X) = 5(1-p)^10 (since each box has the same probability of being empty)

Substituting ∑(i = 1 to 5) p = 1, we get p = 1/5. Therefore,

E(X) = 5(1-1/5)^10 = 5(4/5)^10 ≈ 0.328

So, the expected number of boxes that do not have any balls is approximately 0.328.

(b) Let Y be the number of boxes that have exactly one ball. The probability that a particular box has exactly one ball is given by:

P(exactly one ball in a box) = 10p(1-p)^4

where p is the probability that a ball is put into that box. The expected number of boxes that have exactly one ball is then:

E(Y) = 5(10p(1-p)^4)

Substituting p = 1/5, we get:

E(Y) = 5(10/5^5) = 1/25

So, the expected number of boxes that have exactly one ball is 1/25.

Answer:

The function is increasing for all real values of x where

–6 < x < –2.

Answer:

k

Step-by-step explanation:

c. $1,293.40 is the Santos's monthly Social Security benefit, after delaying collecting for 2 years.

If Santos delays collecting his Social Security benefits for 2 years, he will be eligible for delayed retirement credits. The amount of the increase depends on his birth year and the specific rules in place at the time. As of my knowledge cutoff in September 2021, for individuals born in 1943 or later, the delayed retirement credit is 8% per year for each year of delay beyond full retirement age.

Assuming Santos's original benefit at full retirement age was $1,115.00, we can calculate the increase after a 2-year delay:

Increase = Original Benefit * (Delayed Retirement Credits per year * Number of years of delay)

Increase = $1,115.00 * (0.08 * 2)

Increase = $1,115.00 * 0.16

Increase = $178.40

To calculate Santos's monthly Social Security benefit after the 2-year delay, we add the increase to his original benefit:

New Benefit = Original Benefit + Increase

New Benefit = $1,115.00 + $178.40

New Benefit = $1,293.40

Santos's monthly Social Security benefit, after delaying collecting for 2 years, would be approximately $1,293.40. Therefore, Option c is correct.

The question was incomplete. find the full content below:

Calculate Santos's monthly Social Security benefit if he delays collecting for 2 years and his original benefit at full retirement age was $1,115.00.

a. $1,156.90

b. $1,209.35

c. $1,293.40

d. $1,315.50

Know more about Social Security benefit here:

https://brainly.com/question/29798181

#SPJ8

The two different quantities to measure which school has higher academic performance are :

• Graduation rate / Budget per student

• SAT average / Budget per student

To specify a number that represents academic achievement. We compare the budget per pupil for each school to a related metric or parameter that measures the academic performance of the students in each school.

The following variables could be used to gauge academic achievement:

• Each school's graduation rate.

• Each school's average SAT score.

Therefore, Graduation rate / Budget per student and SAT average / Budget per student are appropriate in this case.

Learn more about ratio on:

https://brainly.com/question/2328454

#SPJ1

Answer:

Therefore, at x=0, -1, 1 , f(x) will be 0 . Hence, 0, -1 ,1 are the x-intercepts.

Plotting the graph on desmos, the graph will be as in the attachme

Step-by-step explanation:

f(x)=x^4+x^3-x^2-x

=x^3(x+1)-x(x+1)

=(x+1)(x^3-x)

=(x+1)x(x^2-1)

=(x+1)x(x+1)(x-1)

=(x+1)2x(x-1)

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

To learn more about modulus function click :

https://brainly.com/question/13682596

#SPJ9

The average speed on the first 30 minutes is 0.2 km per min.

Here we have the graph for the position of a bycicle rider on a 42-minute trip.

On the vertical axis we can see the position, and on the horizontal axis we can see the time.

Remember that:

speed = distance/time.

To find the average speed on the first 30 min, we need to take the quotient between the position after 30 minutes and 30 min.

At 30 min we can see that the position is at 6 km, then the speed will be:

S = 6km/30min = 0.2 km per min.

Learn more about speed at:

https://brainly.com/question/4931057

#SPJ1

45, 28, 53

The pythagorean triple is an equation of the form:

a² + b² = c²

Since the question states that the set of numbers are possible side lengths of a Pythagorean triple, the longest value in the set will be considered as the hypotenuse.

Considering the sets one after the other:

For the set (18, 24, 42)

18² + 24² ≠ 42²

For the set (45, 28, 53)

45² + 28² = 53²

Since this obeys a² + b² = c², the set (45, 28, 53) forms a Pythagorean triple.

All other sets do not obey the rule a² + b² = c², therefore, they do not form the Pythagorean triple.

y = 3

y = 9

For two lines to be parallel, their slope must be equal.

Now, we are told the lines have opposite slopes. This means the slopes are 0.

This because the slopes need to be the same and be opposite to each other.

The only number with this characteristic is 0.

The opposites are 0 and -0. Both are equal to zero.

The equation of line with slope zero, will have a constant y coordinate.

This because: y = mx + c

when m = 0, we will be left with:

y = c = y-intercept

GIven poin: (2, 3) = (x, y)

In our question, the y coordinate from the point given is 3

The equation of one the line: y = 3

we are told the sum of the y intercept of both lines = 12

since the first y-intercept = 3

1st y-intercept + 2nd y- intercept = 12

The second y-intercept = 12 - 3 = 9

slope of the second one is also 0, y = c = y-intercept

The equations of the line:

y = 3

y = 9

we complete the sentence:

The equations of the lines are y = 3 and y = 9; parallel lines have same slopes;

So if slopes are opposites, the slopes must be zero. A line with the slope and passing through (2, 3) has an equation y = 3

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

9 minutes

Step-by-step explanation:

We can start by dividing 45 by 5, the denominator which is

9

then we can multiply that by the numerator 4, which is

36

finally, we subtract 36 from 45 which is

9