how many times does 5.4 go into 60 if it starts at -18?

Answer:

The two pieces of information are needed to prove that line AB is a perpendicular bisector of line CD are:

m∠AGD = 90° ⇒ B

CG = GD ⇒ C

Step-by-step explanation:

If line m is the perpendicular bisector of line AB and intersect it at point D

Let us use these facts to solve our question

Look at the given figure

∵ Line AB is the perpendicular bisector of line CD

∵ Line AB intersects line CD at point G

∴ G is the midpoint of CD

→ That means the point G divides the line CD into two equal parts

   CG and GD

∴ CG = GD

∵ AB ⊥ CD at G

∴ ∠AGD and ∠AGC are right angles

→ the measure of the right angle is 90°

∴ m∠AGD = m∠AGC = 90°

The two pieces of information are needed to prove that line AB is a perpendicular bisector of line CD are:

m∠AGD = 90° ⇒ B

CG = GD ⇒ C

Answer:

Option B is correct

(a)The corresponding accumulation function a(t) is obtained by integrating A(t) with respect to t. Integration is the reverse process of differentiation, i.e., it undoes the effect of differentiation.

= ∫(t²+2t+4)dt

= [t³/3+t²+4t]+C         , where C is the constant of integration.

Thus, the accumulation function a(t) is given by         a(t) = ∫(t²+2t+4)dt = t³/3+t²+4t+C

(b)To find ㏑, we integrate the difference between a and b with respect to t and evaluate it between the limits n and 0.

=∫₀ⁿ

=〖(a(t)-b(t)) dt= a(n)-a(0)-[b(n)-b(0)] 〗

= [n³/3+n²+4n]-[0+0+0]-[n²/2-2n-4]

= n³/3+3n²/2+6n-4

Thus, ㏑= n³/3+3n²/2+6n-4.

learn more about the accumulation function: https://brainly.com/question/12231722

#SPJ11

When a₁ = 4, d = 3.5, and n = 14 are given.The value of A(14) is 49.5, the correct answer is option C. The issue appears to be related to number juggling arrangements, where A(n) speaks to the nth term of the arrangement and a₁ speaks to the primary term of the sequence.

Ready to utilize the equation for the nth term of a math grouping:

A(n) = a₁ + (n-1)d

where d is the common contrast between sequential terms.

A(14) = 4 + (14-1)3.5

Streamlining this condition, we get:

A(14) = 4 + 13*3.5

A(14) = 4 + 45.5

A(14) = 49.5

Hence, the esteem of A(14) is 49.5, which is choice C. 

To learn about sequential terms visit:

https://brainly.com/question/30927272

#SPJ4

if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

To learn more on Angles click:

brainly.com/question/28451077

#SPJ1

The percentage decrease in the price of the two bags of oranges is 25.1 %.

We have been told that the usual price of a bag of oranges was $4 and during the promotion, it became $5.99 for two bags of oranges. We need to find the percentage decrease here.

We can calculate that two bags before the promotion cost =  $4 × 2 = $8

As we already know, the two bags during the promotion cost = $5.99

The decrease in price can be calculated as well  =  $8 - $5.99 = $2.01

Percentage decrease = ($2.01 /  $8) * 100 %

Percentage decrease = 25.1 %

Learn more about percentages on

https://brainly.com/question/29306119?referrer=searchResults

#SPJ4

Instead of using a t-test, alternative statistical tests can be employed when the null hypothesis makes specific claims about the data. These tests are chosen based on the type of data and the specific hypothesis being tested.

When the null hypothesis makes claims about the data that go beyond a simple comparison of means, using a t-test may not be appropriate. Alternative statistical tests can be used in such situations to address specific hypotheses.

For example, if the null hypothesis involves comparing proportions, a chi-square test or Fisher's exact test can be used. These tests are suitable for analyzing categorical data and determining if there is a significant difference between observed and expected frequencies.

Similarly, if the null hypothesis involves comparing means across more than two groups, analysis of variance (ANOVA) or its non-parametric counterpart, the Kruskal-Wallis test, can be employed. These tests allow for the comparison of means across multiple groups and can provide valuable information about the overall differences between groups.

The selection of an appropriate test depends on various factors. The nature of the variables being analyzed, such as categorical or continuous, influences the choice of test. Sample size also plays a role, as some tests require larger sample sizes to yield accurate results. Additionally, each test has certain assumptions associated with it, and researchers need to ensure these assumptions are met before applying the test.

By using alternative tests that are suitable for the specific hypotheses being tested, researchers can gain a deeper understanding of their data. This approach allows for more accurate statistical inferences and can provide valuable insights into the relationships and differences present in the dataset.

To learn more about ANOVA click here, brainly.com/question/31809956

#SPJ11

The circumference of the circular test track is 3.3 km. When a car travels around the track from the southernmost point to the northernmost point, it covers the entire circumference of the track.

To calculate the distance traveled by the car, we can use the formula: distance = circumference.

In this case, the distance traveled by the car is equal to the circumference of the track, which is 3.3 km.

So, when the car completes one full lap around the track, it will have traveled a distance of 3.3 km.

If the car completes multiple laps around the track, the total distance traveled will depend on the number of laps. For example:

- If the car completes 2 laps, the total distance traveled will be 2 times the circumference, which is 2 * 3.3 km = 6.6 km.
- If the car completes 3 laps, the total distance traveled will be 3 times the circumference, which is 3 * 3.3 km = 9.9 km.

Therefore, the distance traveled by the car around the circular test track depends on the number of laps completed.

To know more about distance traveled, visit:

https://brainly.com/question/12696792

#SPJ11

SOLUTION

We will be pairing the pumpkins as follows

AB, CD, EF and GH

For AB, we have

Hence B is 3 times larger than A

For C and D, we have

Hence D is 5 times larger than C

E and F, we have

Hence E is 4.583 times larger than F

And the last G and H, we have

Hence G is 2.167 times larger than H

Step-by-step explanation:

the first one

10 - 4x - 5 + 2x

-4x + 2x = -2x

10 - 5 = 5

so, in sum,

-2x + 5

Answer:

Yes

Step-by-step explanation:

If you find the value of all the angles, you'll find that both triangles' angles are 50, 35, and 90 degrees.

(all the angles in a triangle add up to 180)

Answer:

The answer is 55 degrees.

Step-by-step explanation:

As shown by the red box on the angle, the angle shown is a right angle and is 90 degrees. Because we know the total angle measure, we can subtract the 31 degree angle from the 90 degree angle, which leaves us with 59 degrees for the second angle. This second angle equals (x+4). We then solve for x by setting up the equation 59= x+4. Subtract 4 from both sides and you are left with 55 degrees for x.

Answer:

The answer is 55 degrees.

Step-by-step explanation:

As shown by the red box on the angle, the angle shown is a right angle and is 90 degrees. Because we know the total angle measure, we can subtract the 31 degree angle from the 90 degree angle, which leaves us with 59 degrees for the second angle. This second angle equals (x+4). We then solve for x by setting up the equation 59= x+4. Subtract 4 from both sides and you are left with 55 degrees for x.

We are given the expression √4x^2+100 and the substitution x/5=tan(θ). Our goal is to use the substitution to write the expression as a trigonometric expression and simplify as much as possible.

First, let's substitute x/5=tan(θ) into the expression:

√4(tan(θ)*5)^2+100

Next, let's simplify the expression:

√4(25tan^2(θ))+100

√100tan^2(θ)+100

Now, let's factor out 100 from the expression:

√100(tan^2(θ)+1)

10√tan^2(θ)+1

Finally, let's use the trigonometric identity 1+tan^2(θ)=sec^2(θ) to simplify the expression further:

10√sec^2(θ)

10sec(θ)

Therefore, the expression √4x^2+100 can be written as 10sec(θ) using the substitution x/5=tan(θ).

To learn more about trigonometry here:

https://brainly.com/question/25618616#

#SPJ11

The temperature in the late afternoon is -3°F.

According to the question,

We have the following information:

When Liz woke up in the morning, it was 6°F. By the late afternoon, the temperature had dropped 9°F.

Now, we can easily find the temperature in late afternoon.

To find this, we will have to subtract 9 from 6 because the temperature has dropped from 6.

(Please note that the temperature given here is in ° F. However, it is to be noted that the two most commonly used units of temperature are °F and °C.)

So, we have the following expression:

6-9

-3°F

Hence, the temperature in the late afternoon is -3°F.

To know more about temperature here

https://brainly.com/question/11464844

#SPJ1

(a) To find the 71st percentile, we look up the corresponding z-score using a standard normal distribution table. The closest values to 0.71 are 0.7107 and 0.7112, which correspond to z-scores of 0.54 and 0.55, respectively. Since the value is closer to 0.7107, we use this z-score. Thus, the 71st percentile corresponds to a z-score of 0.54.

(b) Similarly, for the 29th percentile, we look up the corresponding z-score using a standard normal distribution table. The closest value to 0.29 is 0.2881, which corresponds to a z-score of -0.55. Thus, the 29th percentile corresponds to a z-score of -0.55.

(c) To find the 76th percentile, we look up the corresponding z-score using a standard normal distribution table. The closest values to 0.76 are 0.7557 and 0.7611, which correspond to z-scores of 0.68 and 0.69, respectively. Since the value is closer to 0.7611, we use this z-score. Thus, the 76th percentile corresponds to a z-score of 0.69.

(d) Similarly, for the 24th percentile, we look up the corresponding z-score using a standard normal distribution table. The closest value to 0.24 is 0.2394, which corresponds to a z-score of -0.73. Thus, the 24th percentile corresponds to a z-score of -0.73.

(e) To find the 7th percentile, we look up the corresponding z-score using a standard normal distribution table. The closest value to 0.07 is 0.0694, which corresponds to a z-score of -1.51. Thus, the 7th percentile corresponds to a z-score of -1.51.

Note: Interpolation is used to estimate values that are not explicitly listed in the standard normal distribution table. To interpolate, we find the closest values in the table and estimate the value in between them using the proportionality of the standard normal distribution.

For more details about percentile click here:

https://brainly.com/question/13638390#

#SPJ11

Answer:

Step-by-step explanation:

We have pairs (5, 2550) and (8, 3300)

Find the rate of change:

$250 is the amount added to savings account every month

Initial amount was:

Since the change is linear and we have y-intercept and slope, we can show the amount after x months as:

Step-by-step explanation:

i think the answer is 7 yes it has to be 7

Answer:

B

Step-by-step explanation:

To find the x- intercepts let f(x) = 0 , that is

(x + 1)(x + 4) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 1 = 0 ⇒ x = - 1

The x- intercepts are (- 4, 0 ) and (- 1, 0 )

a) T(z) is increasing: (0, π), (2π, 3π), ...

b) T(z) is decreasing: (π, 2π), (3π, 4π), ...

c) T(z) is concave up: (0, π/2), (2π, 5π/2), ...

d) T(z) is concave down: (π/2, 2π), (5π/2, 4π), ...

e) Absolute minimum: T(-3) at z = -3

f) Relative maximum: T(8) at z = 8

What is concave up/down?

Concave up and concave down refer to the shape of a curve or graph.

Concave up (also known as convex) describes a curve that is curved upwards, forming a "U" shape. It means that the graph is curving upward as we move from left to right.

Concave down (also known as concave) describes a curve that is curved downwards, forming an inverted "U" shape. It means that the graph is curving downward as we move from left to right.

To identify the intervals where the given function \(T(z) = sin^2(z/4)\)satisfies the conditions of being increasing, decreasing, concave up, and concave down, as well as finding the absolute minimum and relative maximum, we need to analyze the first and second derivatives of the function.

First, let's find the first derivative of T(z):

\(T'(z) = (2/4)sin(z/4)cos(z/4) = (1/2)sin(z/2)cos(z/2) = (1/4)sin(z)\)

Now, let's find the second derivative of T(z):

\(T''(z) = (1/4)cos(z)\)

a) T(z) is increasing:

T'(z) > 0 or T''(z) > 0

Interval: (0, π), (2π, 3π), ...

b) T(z) is decreasing:

T'(z) < 0 or T''(z) < 0

Interval: (π, 2π), (3π, 4π), ...

c) T(z) is concave up:

T''(z) > 0

Interval: (0, π/2), (2π, 5π/2), ...

d) T(z) is concave down:

T''(z) < 0

Interval: (π/2, 2π), (5π/2, 4π), ...

e) Absolute minimum and its location:

The absolute minimum occurs at the lowest point of the function.

Absolute minimum value: \(T(-3) = sin^2((-3)/4)\)

Location: z = -3

f) Relative maximum and its location:

The relative maximum occurs at the highest point of the function, excluding the absolute minimum.

Relative maximum value: \(T(8) = sin^2((8)/4)\)

Location: z = 8

Please note that the intervals mentioned are based on the given range -3 ≤ z ≤ 8.

To know more about concave up/down visit:

https://brainly.com/question/15088275

#SPJ4

Answer and Step-by-step explanation: The triangles are plotted and shown in the attachment.

SAS Similarity Theorem is by definition: if two sides in one triangle are proportional to two sides of another triangle and the angles formed by those sides in each triangle is congruent, the triangles are similar.

For the triangles on the grid, we know that ΔJKL and ΔJMN have a congruent angle in J as shown in the image. To prove they are similar, we find the slope of sides KL and MN:

Slope of KL:

slope = \(\frac{y_{K} - y_{L} }{x_{K} - x_{L} }\)

slope = \(\frac{3-1}{2-4}\)

slope = -1

Slope of MN:

slope = \(\frac{y_{N} - y_{M} }{x_{N} - x_{M} }\)

slope = \(\frac{1-5}{7-3}\)

slope = -1

Since the slopes of KL and MN are the same and the angle is congruent, we can conclude that ΔJKL~ΔJMN.

Answer:

The anwser is 6.01176470588

Answer:

68%

Step-by-step explanation:

In normal distribution, the empirical rule (aka 68-95-99.7 rule) describes the approximate proportion of data that falls within certain distances from the mean of a normal distribution. Specifically, the rule states that:

The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

An equation is an expression that shows the relationship between two or more numbers and variables.

A unit rate is a ratio between two different units with a denominator of one.

If For every 1 student out of school, there are 10 students going to school, hence:

Unit rate = 10/1 = 10 students going to school per 1 student out of school

The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

389 hours and 23 minutes

Step-by-step explanation:

16x24=384

384+=5=389

and 23 minutes

Unit conversion is the conversion of one unit to another unit with its standard conversion.

The distance traveled in 15 minutes at a speed of 12m/s is 10800 m.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 minute = 60 seonds

1 km = 100 m

1 m = 100 cm

We have,

Speed = 12 m/s

This means,

1 second = 12 m

Now,

1 minute = 60 seconds

15 minutes = 15 x 60 seconds

15 minutes = 900 seconds

So,

1 sec = 12 m

Multiply 900 on both sides.

900 x 1 sec = 900 x 12m

900 seconds = 10800 m

Thus,

The distance traveled in 15 minutes at a speed of 12m/s is 10800 m.

Learn more about unit conversion here:

https://brainly.com/question/13899873

#SPJ1

Answer:

36 kg

Step-by-step explanation:

Make a conversion factor.  If 15 units = 90 kg, then 90 kg/15 units = 6kg/unit.

(6kg/unit)*(6 units) = 36 kg

The linear inequalities are a ≤ 2j+3 , j≥14 ,a≤35 , Therefore Option C is the correct answer.

Inequality can be defined as a mathematical statement where the algebraic expression are equated by an inequality Operator , < , > ,<> etc.

It is given in the question that

Anna is no more than 3 years older than 2 times jamie’s age.

Let Anna's age be a and Jamie's age is j

then

a ≤ 2j+3

jamie is at least 14 and anna is at most 35

j≥14

a≤35

The linear inequalities are a ≤ 2j+3 , j≥14 ,a≤35

Therefore Option C is the correct answer.

To know more about Inequality

https://brainly.com/question/20383699

#SPJ1

Answer:

b

Step-by-step explanation:

Answer:

(2d +3d) + 3-12 equals to 5d - 9

Step-by-step explanation:

you try collecting like terms

Answer:

\(5d-9\)

Step-by-step explanation:

Given the following question:

\((2d + 3) + (3d-12)\)

To find the answer remove the parentheses, group like terms, and solve by using inverse of operations.

\((2d + 3) + (3d-12)\)
\(2d+3+3d-12\)
\(2d+3d+3-12\)
\(3-12=-9\)
\(2d+3d+-9\)
\(2d+3d=5d\)
\(5d-9\)

Your answer is "5d - 9."

Hope this helps.