1. Which of the following is an example of like
terms?
a. - 16 and - 16x
b. x and x2
C, 50y and y
d. 20a and 2

The measure of angle B where angle B is an acute angle by using the Law Of Sines is 61° .

What is an Acute Angle ?

The Acute Angle can be defined as an angles that measure less than 90° , the acute angle is smaller than Right Angle and also smaller than the Linear Angle ( measuring 180° ).

From the figure ,

we can see that the measure of the sides are given as a = 9 , b = 8 and

the measure of angle A is 79° .

By Applying the Law Of Sines ;

we get ,

\(\frac{SinA}{a} =\frac{SinB}{b}\)

Substituting the values in the above equation ,

we get ;

\(\frac{Sin79\textdegree}{9} =\frac{SinB}{8}\)

Simplifying further ,

we get ;

\(SinB = \frac{Sin79\textdegree}{9} \times 8\)

substituting the value of Sin79° as 0.9816 ;

we get ;

\(SinB = \frac{0.9816}{9} \times 8\)

\(SinB=0.8725\)

So , B ≈ 61° .

Therefore , the measure of angle B is 61° .

The given question is incomplete , the complete question is

Find the measure of Angle B in the given figure .

Note that the angle B is acute . Round to the nearest degree .

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The given linear system can be represented as a matrix equation:

A * X = B

where `A` is the coefficient matrix, `X` is the variable matrix, and `B` is the constant matrix.

The augmented matrix for the system is:

[-6 1 4 -2 | 1]

Using Gaussian elimination or row reduction, we can transform the augmented matrix to its row-echelon form:

[1 -1/6 -2/3 1/3 | -1/6]

[0 1 2/3 -1/3 | 1/6]

[0 0 0 0 | 0 ]

This row-echelon form implies that the system has a dependent variable since the third row consists of all zeros. In other words, there are infinitely many solutions to the system. The dependent variable, denoted as `x3`, can be expressed in terms of free parameters `s1` and `s2`.

Therefore, the set of solutions to the given linear system is:

x1 = -1/6 + (2/3)s1 - (1/3)s2

x2 = 1/6 - (2/3)s1 + (1/3)s2

x3 = s1

x4 = s2

where `s1` and `s2` are arbitrary real numbers that serve as parameters. These equations represent the general form of the solution, accounting for the infinite possible solutions.

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Using the z-distribution, as we are working with a proportion, the 90% confidence level estimate for the true proportion of employees in the district who have gotten a flu shot is (0.2355, 0.4784).

As long as there are 10 successes and 10 failures in the sample, that is, \(n\pi \geq 10\) and \(n(1 - \pi) \geq 10\), a confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, the parameters are:

\(n = 42, \pi = \frac{15}{42} = 0.3571, z = 1.645\)

We have the \(n\pi = 15, n(1 - \pi) = 27\), hence you can find the interval.

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3571 - 1.645\sqrt{\frac{0.3571(0.6429)}{42}} = 0.2355\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3571 + 1.645\sqrt{\frac{0.3571(0.6429)}{42}} = 0.4787\)

The 90% confidence level estimate for the true proportion of employees in the district who have gotten a flu shot is (0.2355, 0.4784).

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Unit rate for first graph = 52 mph

Unit rate for 2nd graph = 67 mph

The two graphs given plot two linear relationships between Distance travelled (mi) and Time (hr.). We need to find the unit rate for each.

Unit rate is the speed calculated when the time is unity, i.e., when time = 1 hr. on both the graphs.

On the first graph the co-ordinate marked is (1,52), which implies the Distance travelled = 52 miles and Time = 1 hr

So the speed = Distance travelled/ Time

                      = 52/1

                      = 52 mph

Thus, the unit rate = 52 mph

On the second graph two co-ordinates are given which are (3,201) and (4,268).

Consider any one co-ordinate to find the speed in this case. Also this speed will be constant as the graph is a straight line between the Distance travelled and the Time.

So consider (3,201) which means Distance travelled = 201 miles and Time = 3 hr

So the speed = Distance travelled/Time

                       = 201/3

                       = 67 mph

Unit rate is the speed when time = 1 hr

Since this speed is constant everywhere on the second graph, the speed when time = 1 hr is also 67 mph.

Hence the unit rate = 67 mph

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Answer:

B) 2

Step-by-step explanation:

a3 = 7 , d = -5 (GIVEN)

a4 = a3 + d

= 7 + (-5)

= 7 - 5

a4 = 2

HOPE IT HELPS (✷‿✷)

Answer:

\(\Huge \boxed{a_4=2}\)

Step-by-step explanation:

The third term in an arithmetic sequence is 7.

The common difference is -5.

The common difference of an arithmetic sequence is found by subtracting a term in the sequence with the previous term.

\(d=a_4-a_3\)

Solving for the fourth term.

\(a_4 = a_3 + d\)

Plugging in the values and evaluating.

\(a_4=7+-5\)

\(a_4=2\)

The value of the fourth term is 2.

Answer:

It takes 22.52 years for the balance to triple in value.

Step-by-step explanation:

Continuous compounding:

The amount of money earned using continuous compounding is given by the following equation:

\(A(t) = A(0)(1+r)^t\)

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.

Interest rate of 5%.

This means that \(r = 0.05\), and thus:

\(A(t) = A(0)(1+r)^t\)

\(A(t) = A(0)(1+0.05)^t\)

\(A(t) = A(0)(1.05)^t\)

Time for the balance to triple?

This is t for which \(A(t) = 3A(0)\). So

\(A(t) = A(0)(1.05)^t\)

\(3A(0) = A(0)(1.05)^t\)

\((1.05)^t = 3\)

\(\log{(1.05)^t} = \log{3}\)

\(t\log{1.05} = \log{3}\)

\(t = \frac{\log{3}}{\log{1.05}}\)

\(t =  22.52\)

It takes 22.52 years for the balance to triple in value.

Answer:

9

Step-by-step explanation:

the expression is 2ac, so multiply everything together

2 * 1/2 = 1

1 * 9 = 9

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Margin of error is statistical expressing the amount of a random sampling error in survay results not the error term from biased sampling method. So, correct answer is False.

Margin of error in statistics represents the amount of random sampling error in the survey results. The larger the margin of error, the less confident that the survey results reflect the results of the census of the entire population. It is denoted by E or MOE. It is calculated by dividing the square root of the sample size by the standard deviation of the population. 99% level is the most conservative, 90% level is the least conservative. The sampling error is a statistical error that occurs when the analyst does not select a sample that is representative of the entire data population.

False - Margin of error only account for sample variability (the fact that my sample differs from many others' samples and therefore provides different statistics.

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When rolling a number cube one time, there are several things that are true. Here are three options:

1. The outcome will be a whole number between 1 and 6: Since the number cube has faces numbered from 1 to 6, rolling it one time will result in one of these whole numbers.

2. Each face has an equal chance of landing face-up: The number cube is designed in such a way that each face has an equal probability of landing face-up when rolled. This means that the chances of rolling a 1, 2, 3, 4, 5, or 6 are all the same.

3. The outcome is independent of previous rolls: Rolling the number cube one time does not depend on or affect any previous rolls. Each roll is considered an independent event, so the previous outcome does not influence the next roll.

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The value of the test​ statistic is - 0.462.

A standard deviation (or) would be a way of measuring of how widely distributed the data has been in relation towards the mean. A low standard deviation indicates that data is grouped around the mean, whereas a high standard deviation indicates that data is more spread out.

The null hypothesis is:

H0 = 0.25

The alternate hypothesis is:

H1 does not equal to 0.25,

the general formula for standard deviation is :-

σ=√1N∑Ni=1(Xi−μ)2 σ = 1 N ∑ i = 1 N ( X i − μ ) 2.

Our test statistic is:

t = (x- u) /s

In which X is the sample mean,  u is the population mean(the null hypothesis),   s is the standard deviation of the sample.

According to question,

x = 23/100

x = 0.23

u = 25/100

u= 0.25

s= √(0.25 * 0.75)/100

s = 0.0433

so for the value of t,

standard deviation = (x - u)/t

so , t=  (x- u) /s

t = (0.23 - 0.25)/0.0433

t = - 0.462

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Answer:

19

Step-by-step explanation:

\(f(2)=2(3^2)+1=2(9)+1=18+1=\boxed{19}\)

A:

4 seconds per centimer:

30cms               15 cms

----------------       -------------

2 minutes           1 minute

1 minute= 60 seconds

15 cms                       1cm

-----------------     =     ----------------

60 seconds              4seconds

B: 15 cms per minute

30cms/2minutes

(divide by 2 to get speed for one minute)

15cm/1 minute

Answer:

the thrid one

Step-by-step explanation:

The table that shows a function that is decreasing only over the interval (-1, oo) is table 3

For a table to show a decreasing interval, then the table values must reduce as the x value increase

The interval (-1, oo) means that, -1 is exclusive of the x values.

So, we start from x > -1

The first table shows an increasing function for x > -1

The second table shows an increasing and decreasing function for x > -1

The third table shows a decreasing function for x > -1

The last table shows a decreasing function for x > -1 but increases at other values

Hence, the table that shows a function that is decreasing only over the interval (-1, oo) is table 3

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Therefore, the distance that Caleb skated in one lap by skating along the edge of the rink is 70 feet.

The distance that Caleb skated one lap by skating along the edge of the circular rink can be calculated using the formula for the circumference of a circle, which is C = 2πr. Since the rink measures 70 feet from side to side, the radius (r) of the circle can be found by dividing this measurement by 2, which gives 35 feet.

Plugging this value of r into the formula, we get:

C = 2π(35)
C = 70π

So the circumference of the circular rink is 70π feet. Therefore, the distance that Caleb skated one lap by skating along the edge of the rink is 70π feet.

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Answer: Should be 140000 cm

Step-by-step explanation:I may be wrong but 240 x 5 is 1400 and that to cm is 140000

Answer:

60,000 cm

Step-by-step explanation:

1 m = 100 cm

So, 120 m = 12,000 cm.

120 m (5 times) = 600 m

600 m = 100 (600)

            = 60,000 cm

Answer: Figure B is 2x bigger on all sides

Explanation: You can see that each of the numbers times 2 would equal all of the numbers on B.

The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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Answer:

11x+2

Step-by-step explanation:

If two lines intersect, then the vertical angles formed must be both equal in measure.

The  intersection of a line can be described as when two or more lines cross each other in a plane as a result of this they are been referred to as   intersecting lines.

Therefore, intersecting lines share a common point, hence , If two lines intersect, then the vertical angles formed must be both equal in measure.

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Answer:

22.50 + 9.50x = 165

*** x represents the number of shirts he's buying***

If 66 sixth graders are randomly selected, the probability that the sample mean would be greater than 92.25 wpm is approximately 0.2142 or 21.42%.

If the sample size is sufficient, we can apply the theorem of central limitation to determine the pattern of distribution of sample means. Since n = 66 is a big enough number in this situation, we may use a normal distribution to roughly comparable the distribution of the sample means.

The general population's mean, which is 89 wpm, is the same as the mean value of the sample means. The following formula can be used to identify the average deviation of the sample means, commonly referred to as the standard deviation or error of the mean:

Standard error is equal to standard deviation squared.(sample size) Standard deviation: 16 squared(66) standard deviation: 1.969 Using the following formula, we can now standardise the sample mean: The formula for z is (sample mean - population mean) / standard error. z = (92.25 - 89) / 1.969 z = 1.732

We may determine the probability when a standard normal random variable is greater than 1.732 using the standard normal distribution table or calculator. This likelihood is roughly 0.0429, or 4.29%. we must remember that rather than just looking for any random variable, we are seeking for the probability that a sample mean is higher than 92.25 wpm. As a result, we must use the sample mean distribution, which we roughly categorized as a normal distribution.

The z-score must then be converted using the following formula to its original units of measurement: Sample mean equals population mean plus z times the standard error. 89 + 1.732 * 1.969 is the sample mean.

92.25 is the sample mean.

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Answer:

14 mph

Step-by-step explanation:

Speed of boat in calm water = x

Speed of current = y

Speed of boat with the current = 72 mi / 4 hr = 18 mph

Speed of boat against current = 40 mi / 4 hr = 10 mph

x + y = 18

x - y = 10

2x = 28

x = 14

Answer: 14 mph

Answer:

14 m/hr

Step-by-step explanation:

72 m / 4 hr = 18 m/hr

40 m / 4 hr = 10 m/hr

still water speed =  (18+ 10 )/2 = 14 m/hr

 current speed   (14 -x) 4 = 40

                       x = current speed = 4 m/hr

The measure of angle C in radians is 3.6 radians.

The arc length of a circle is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.

Given that, the circle has a radius of 7 and angle C intercepts the arc with a length of 28π.

We know that, formula to find the arc length of circle is Arc length= θ/360 ×2πr

28π= θ/360×2π×7

4= θ/360×7

θ=1440/7

θ=205.7

θ=3.6 radians

Therefore, the measure of angle C in radians is 3.6 radians.

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Answer:

Step-by-step explanation:

4 miles plus 2 miles equals 6 miles, then you add 7 miles to the 6 which equals 13, lastly you minus 13 from 30 then you get your answer, which is 17.

36/60

=0.6

60% is your answer

Answer:

a. x^2 - 1

b. x^2 - 6x + 9

c. \(\dfrac{3x + 1}{x^2 + x}\)

Step-by-step explanation:

a.

(x + 1)(x - 1) =

= x^2 - x + x - 1

= x^2 - 1

b.

(x - 3)^2 =

= (x - 3)(x - 3)

= x^2 - 3x - 3x + 9

= x^2 - 6x + 9

c.

\( \dfrac{3 + \frac{1}{x}}{1 + x} = \)

\( = \dfrac{x(3 + \frac{1}{x})}{x(1 + x)} \)

\( = \dfrac{3x + 1}{x + x^2} \)

\( = \dfrac{3x + 1}{x^2 + x} \)

Answer:

B

Step-by-step explanation:

V26 is closer to 5 because it's only one number away.

The number among the option that is closest to 5 is √26.

The number closest to 5 is the number that is almost 5.

The option are express in surd form, therefore, lets express in real numbers(decimal form) Real numbers are rational or irrational numbers. Therefore,

√23 = 4.79583152331

√26 = 5.09901951359

√22 = 4.69041575982

√28 = 5.29150262213

Therefore, using the decimal form, the closest number to 5 is √26

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The approximate probability of getting a z-score between +1 standard deviation and +2.5 standard deviations in a standard normal distribution is 0.1525.

To find the area under the standard normal curve between +1 standard deviation and +2.5 standard deviations, we can use a standard normal distribution table or calculator. Here are the steps:

Therefore, the area under the standard normal curve between +1 standard deviation and +2.5 standard deviations is approximately 0.1525.

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Using Euler's method with a step size of 0.2, the estimated value of y(1) for the initial-value problem y' = x^2 + xy, y(0) = 5 is approximately 7.0096.

Euler's method is a numerical approximation technique used to estimate the solution of a first-order ordinary differential equation (ODE) given an initial condition. In this case, we are solving the initial-value problem y' = x^2 + xy with the initial condition y(0) = 5.

To apply Euler's method, we start with the initial condition. Since we have a step size of 0.2, we will divide the interval [0, 1] into five equal subintervals (0.2, 0.4, 0.6, 0.8, 1.0). At each step, we calculate the slope of the ODE at the current point and use it to estimate the change in y over the step size.

Starting with y(0) = 5, we calculate the value of y(0.2) using Euler's method. Then, using this new value of y, we calculate y(0.4), and so on until we reach y(1.0).

Performing the calculations, the estimated value of y(1) using Euler's method with a step size of 0.2 is approximately 7.0096 (rounded to four decimal places).

It's important to note that Euler's method provides an approximate solution, and the accuracy of the estimate depends on the step size chosen. Smaller step sizes generally yield more accurate results.

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