solve this please!!!!!!!!!!

Answer:

x = 19.6

Step-by-step explanation:

By applying cosine rule in ΔBCD,

cos(30)° = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

              = \(\frac{BC}{BD}\)

\(\frac{\sqrt{3}}{2}=\frac{BC}{16}\)

BC = \(8\sqrt{3}\)

Now, by applying sine rule in ΔBAC,

sin(45)° = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

\(\frac{1}{\sqrt{2}}=\frac{AB}{BC}\)

\(\frac{1}{\sqrt{2}}=\frac{x}{8\sqrt{3}}\)

x = \(8\sqrt{6}\)

x = 19.59

x ≈ 19.6  

Answer:

The slope is -6 and the y intercept is 0

Total integers between 30 and 50, inclusive, and 21 - 5 = 16 integers that are not possible total scores.

For a score of 30, the number of correct answers would be 6 (30 / 5), and for a score of 50, the number of correct answers would be 10.

Thus, the possible number of correct answers is between 6 and 10, inclusive. So, the possible total scores are [30, 35, 40, 45, 50].

Therefore, there are 50 - 30 + 1 = 21 total integers between 30 and 50, inclusive, and 21 - 5 = 16 integers that are not possible total scores.

Learn more about Inclusive problems visit the link:

https://brainly.com/question/29227151

#SPJ4

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

learn more about Chi-Square here: brainly.com/question/24976455

#SPJ11

Answer:

Q19 - x = 7

Q20 - x = 24

Step-by-step explanation:

Q19.

75 + x + 8 = 90°

83 + x = 90°

x = 90 - 83

x = 7

{CHECK: 75 + 7 + 8 = 90°}

Q20.

3x - 6 + x = 90°

4x - 6 = 90°

4x = 96

x = 96 / 4

x = 24

{CHECK: 3(24) - 6 + 24 = 90°}

hope this helps...

have a great day ahead ;)

The inverse function over the domain is f⁻¹(x)  = √[(x + 1)/3]

The domain and the range are x ≥ -1 and y ≥ 0

The graph of f(x) = 3x² - 1 and f⁻¹(x)  = √[(x + 1)/3] is added as an attachment

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

f(x) = 3x² - 1

So, we have

y = 3x² - 1

Swap x and y

x = 3y² - 1

Next, we have

3y² = x + 1

This gives

y² = (x + 1)/3

So, we have

y = √[(x + 1)/3]

This means that the inverse function is f⁻¹(x)  = √[(x + 1)/3]

For the domain, we have

x + 1 ≥ 0

So, we have

x ≥ -1

For the range, we have

y ≥ 0

The graph of f(x) = 3x² - 1 and f⁻¹(x)  = √[(x + 1)/3] on the same set of axes is added as an attachment

Read more about inverse function at

https://brainly.com/question/3831584

#SPJ1

There are 402.28 in2 of pasta in the container.

The mathematical branch is known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

The radius of cylinder (r) = 3.2 inches

Height of cylinder (h) = 14 inches

Height of pasta = 14 – 1.4 = 12.5 inches

Pasta in container = 22/7*(3.2)2*12.5

=402.8 in2

Hence, the container carries 402.8 in2 of pasta in it.

To learn more about Algebra, visit:

brainly.com/question/13715639

#SPJ1

Answer:

Step-by-step explanation:

volume of reqd. figure=10×5×1+3×3×1=50+9=59 cm³

Answer:

124.6

Explanation:

Let the number be x.

Thus, we have that: 13% of x =16.2

Next, solve for x by cross-multiplying.

Divide both sides by 13.

Thus, 16.2 is 13% of 124.6 (rounded to the nearest tenth).

Accοrding tο the data, cοpper has a density οf 3 g/cm³.

A basic fοrmula fοr vοlumes is length, breadth, and height, as οppοsed tο length, width, and height fοr the surface οf a rectangle. It dοesn't matter hοw yοu reference tο the variοus dimensiοns; yοu cοuld, fοr instance, use "depth" instead οf "height" withοut the calculatiοn changing.

We must first determine the vοlume οf a cοpper blοck in οrder tο determine its density. A rectangular blοck's vοlume is determined by:

Vοlume = Length x Width x Height

The dimensiοns in this instance are 8 cm lοng, 5 cm wide, and 4 cm high. As a result, the blοck's vοlume is:

Vοlume = 8 cm x 5 cm x 4 cm = 160 cm³

Then, we can use the fοllοwing fοrmula tο get cοpper's density:

Density = Mass / Vοlume

The blοck has a stated mass οf 480 g. Hence, cοpper has the fοllοwing density:

Density = 480 g / 160 cm³ = 3 g/cm³

Sο, the density οf cοpper is 3 g/cm³.

To know more about volume visit:

https://brainly.com/question/1578538?

#SPJ1

The center, vertices, and foci of the given ellipse are as follows:

Center: (-7, -1)

Vertices: (-7, -13) and (-7, 11)

Foci: (-7, -7) and (-7, 5)

The general equation for an ellipse centered at (h, k) with semi-major axis "a" and semi-minor axis "b" is:

(x - h)² / a² + (y - k)² / b² = 1

Comparing this with the given equation, we can see that the center of the ellipse is at (-7, -1).

The semi-major axis "a" is the square root of the denominator of the x-term, which in this case is √225 = 15. So, the vertices will be located 15 units above and below the center. Therefore, the vertices are (-7, -1 - 15) = (-7, -16) and (-7, -1 + 15) = (-7, 14).

The semi-minor axis "b" is the square root of the denominator of the y-term, which in this case is √144 = 12. So, the foci will be located √(a² - b²) units away from the center along the major axis. Using the formula, we find the distance to be √(15² - 12²) = √(225 - 144) = √81 = 9. Therefore, the foci are (-7, -1 - 9) = (-7, -10) and (-7, -1 + 9) = (-7, 8).

In summary:

Center: (-7, -1)

Vertices: (-7, -16) and (-7, 14)

Foci: (-7, -10) and (-7, 8)

To know more about ellipses, refer here:

https://brainly.com/question/20393030#

#SPJ11

Given:

Consider the tank that is filled with water drains at a rate of \(\dfrac{d^2}{16}+4d-100\) gallons per minute where d is the depth of the tank in feet.

Depth of tank = 120 feet.

To find:

The rate of water drain for that tank.

Solution:

We have, rate of water drain in gallons per minute.

\(r=\dfrac{d^2}{16}+4d-100\)

where, d is the depth of the tank in feet.

Put d=120, to get the rate of water drain for the tank.

\(r=\dfrac{120^2}{16}+4(120)-100\)

\(r=\dfrac{14400}{16}+480-100\)

\(r=900+380\)

\(r=1280\)

Therefore, the rate of water drain is 1280 gal/min. Hence, the correct option is B.

The correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

What is property of similar triangle?

If the corresponding sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are similar.

They have parallel corresponding sides, and they have angles with the same measure.

hence, the correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

To learn more about property of similar triangle visit,

https://brainly.com/question/11920446

#SPJ13

Answer:

(\(\frac{-7}{3}\), \(\frac{4}{3}\))

Step-by-step explanation:

Hi there!

We are given the following system of equations:

-3x-3y=3

-5x+y=13

and we need to find the solution (the point at which the 2 lines intersect)  

let's solve this by substitution, where we will set one variable equal to an expression containing the other variable, and then substitute that expression into the other equation to solve for the variable that the expression from earlier contains, and then use the value of the solved variable to find the value of the first variable

in the second equation, add 5x to both sides to isolate y by itself

y=5x+13

now substitute 5x+13 as y in -3x-3y=3

-3x-3(5x+13)=3

do the distributive property

-3x-15x-39=3

combine like terms

-18x-39=3

add 39 to both sides

-18x=42

divide both sides by -18

x=\(\frac{-7}{3}\)

now we need to find y

remember: y=5x+13

substitute \(\frac{-7}{3}\) as x in y=5x+13

y=5(\(\frac{-7}{3}\))+13

multiply

y=\(\frac{-35}{3}\)+13

add

y=\(\frac{4}{3}\)

So the answer is x=\(\frac{-7}{3}\), y=\(\frac{4}{3}\). As a point, it's (\(\frac{-7}{3}\), \(\frac{4}{3}\))

Hope this helps! :)

Step-by-step explanation:

mondey balance 104.24$

Tuesday balancs -23.99$

value = 104.24+23.99=128.23$

Answer:

x° = 54

y = 14

Step-by-step explanation:

Sum of interior angles of a triangle = 180, therefore:

79 + 16 + m∠P = 180

m∠P = 180 - 79 - 16 = 54

m∠RPQ = m∠UST = x° = 54°

64/16 = 28/(y-7)    solve for y:

64(y-7) = (28)(16) = 448

y - 7 = 448/64 = 7

y = 7 + 7 = 14

Answer:

if your looking for the slope it would be 3/1. that is 3 over 1

Answer:

Her utility bill decreased

Step-by-step explanation:

$-9.66 is closer to 0 but before her bill was -$25.66 so that's farther away so her bill decreased.

Nancy’s balance increased: -9.66 > -25.66.

Answer:

Answer:

Step-by-step explanation:

Cos(61) = 0.4848

This is more or less the value of cos(60) which is 1/2

You know you are in trouble when a question says approximately. How approximate is approximately. My guess, and it is a guess, is that this means the nearest degree. That would be 14 degrees. The more exact answer is 13.80 and that zero matters. It is a place holder.

Sin(67) = 0.9205 Again, how approximate is approximate? Try 0.92 as your answer.

Tan (18) = 0.3249 Try tan(18) = 0.3

Answer:

yes

Step-by-step explanation:

yes

Answer:

Ross isn't right.

Step-by-step explanation:

Skateboard $125.95 at 40% off is $75.57

How I got the number:

125.95/100 = 1.2595

1.2595 x 40 = 50.38

125.95 - 50.38 = 75.57

Skateboard $169.95 at 60% off is $67.98

169.95/100 = 1.6995

1.6995 x 60 = 101.97

169.95 - 101.97 = 67.98

Therefore the skateboard that is 60% off is cheaper.

The probability of hitting the bullseye is P(B) = 3/7

Probability is the likelihood of an event.

The probability of an event A is given by P(A) = event space/sample space

Since Samantha is conducting an experiment and has to make a free throw and throw a dart for a bullseye. The probability of accomplishing both is 3 out of 9. The probability of making the free throw is 14 out of 18.

Since the probability of throwing a free throw is indepent of the probability of throwing a dart, they are independent events.

So, the probability for independent events is

P(A ∩ B) = P(A)P(B)

Let

We have that

P(F ∩ B) = P(F) × P(B)

Since we require probability of bullseye, making P(B) subject of the formula, we have

P(B) = P(F ∩ B)/P(F)

Given that

Substituting the values of the variables into the equation, we have

P(B) = P(F ∩ B)/P(F)

P(B) = 1/3 ÷ 7/9

= 1/3 × 9/7

= 3/7

So, P(B) = 3/7

Learn more about probability of independent events here:

https://brainly.com/question/11455301

#SPJ1

The distance between two points in a coordinate plane, you can use the distance formula.  The approximate distance between point L (3, 5) and point M (9, -7) is approximately 13.4 units.

To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and calculates the straight-line distance between two points (x1, y1) and (x2, y2) as follows:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of point L are (3, 5) and the coordinates of point M are (9, -7). Plugging these values into the distance formula, we get:

Distance = √((9 - 3)^2 + (-7 - 5)^2)

= √(6^2 + (-12)^2)

= √(36 + 144)

= √180

≈ 13.4

Therefore, the approximate distance between point L and point M is approximately 13.4 units.

Learn more about Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ11

Answer:

x⊥a

Step-by-step explanation:

If we draw this out, we see that x is perpendicular to a as well.

Answer: 9 13/15

Step-by-step explanation:

Answer:

y=2.5x+9

Step-by-step explanation:

pick any two points and plug 2.5 for x and add 9 to the sum

Answer:

$336.44

Step-by-step explanation:

$402.44 - $66 = $336.44

The odds of selecting a red 9 is 1/26.

Probability of an event E is represented by P(E)  can be defined as (the number of favorable outcomes) / (Total number of outcomes).

Given the total number of cards in a standard deck = 52

there can be  only two red9 as one 9 from heart and one red from diamond.

So the number of outcome for red 9 =2

the probability of odds of selecting red 9 is \(\frac{2}{52}\) which can be further simplified into \(\frac{1}{26}\).

Therefore , The odds of selecting a red 9 is 1/26.

Learn more about Probability here https://brainly.com/question/4446588

#SPJ4