Answer:
x+12=78
Step-by-step explanation:
like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.
Answer:
n + 12 = 78
Step-by-step explanation:
Let n = number.
n + 12 = 78
Starting at point A, a ship sails 18.9 km on a bearing of 190 degrees and then turns and sails 47.2km on a bearing of 318 degrees. Find the distance of the ship from point A. (Use trigonometry)
Answer:
Approximately 38.56 kilometers
Step-by-step explanation:
So, from the picture, we want to find x.
To do this, we can use the Law of Cosines. We simply need to find the angle between the two sides and then plug them into the Law of Cosines. First, the Law of Cosines is:
[tex]c^2=a^2+b^2-2ab\cos(C)\\[/tex]
The c in this equation is our x, and the C is the angle we need to find.
From the picture, you can see that angle C is the sum of the red and blue angles.
From a bearing of 190 degrees, we can determine that the red angle measures 10 degrees. Then by alternate interior angles, the other red angle must also measure 10 degrees.
From a bearing of 318 degrees, the remaining 48 degrees is outside the triangle. However, we have a complementary angle, so we can find the angle inside the triangle by subtracting in into 90. Therefore, the blue angle inside is 90-48=42 degrees.
Therefore, angle C is 42+10 which equals 52 degrees. Now we can plug this into our formula:
[tex]x^2=a^2+b^2-2ab\cos(C)\\\\x^2=(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)\\x=\sqrt{(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)}\\\text{Use a Calculator}\\x\approx38.5566 \text{ km}[/tex]
50q + 43 > −11q + 70
Answer:
q > 27/61
Step-by-step explanation:
50q + 43 > −11q + 70
Add 11 q to each side
50q+11q + 43 > −11q+11q + 70
61q+43> 70
Subtract 43 from each side
61q> 27
Divide each side by 61
61q/61> 27/61
q > 27/61
If h(x)=-2x-10 ,find h(-4)
Answer:
h(-4) = -2
Step-by-step explanation:
h(x)=-2x-10
Let x = -4
h(-4)=-2*-4-10
=8-10
= -2
Answer:
[tex]\huge \boxed{{-2}}[/tex]
Step-by-step explanation:
[tex]\sf The \ function \ is \ given:[/tex]
[tex]h(x)=-2x-10[/tex]
[tex]\sf To \ find \ h(-4), \ put \ x=-4.[/tex]
[tex]h(-4)=-2(-4)-10[/tex]
[tex]h(-4)=8-10[/tex]
[tex]h(-4)=-2[/tex]
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
1256 i think
Step-by-step explanation:
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 8 sin(xy), (0, 9)
Answer:
The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Step-by-step explanation:
Given that:
F(x,y) = 8 sin (xy) at (0,9)
The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]
[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]
[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]
We can conclude that the maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Suppose 65% of people in Georgia support a special transportation tax. Alejandro is not confident that this claim is correct. To investigate the claim, he surveys 150 people in his community and discovers that 78 people support a special transportation tax.
A. calculate sample proportion.
B. calculate standard error of the sample proportion, (SE). Give answer to three decimal places
C. Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
Answer:
C
Step-by-step explanation:
Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
A. The sample proportion is 0.52.
B. The standard error of the sample proportion is approximately 0.041.
C. The standard error of the sample proportion estimate is approximately 0.041.
A. To calculate the sample proportion, we divide the number of people who support the special transportation tax (78) by the total number of people surveyed (150):
Sample proportion = 78 / 150 = 0.52
B. To calculate the standard error of the sample proportion (SE), we use the formula:
[tex]SE = \sqrt{(p * (1 - p)) / n}[/tex]
where p is the sample proportion and n is the sample size. Substituting the values into the formula:
[tex]SE = \sqrt{(0.52 * (1 - 0.52)) / 150}\\\\SE = \sqrt{0.2496 / 150}\\\\SE = \sqrt{0.001664}\\\\SE = 0.0407[/tex]
Therefore, the standard error of the sample proportion is approximately 0.041 (rounded to three decimal places).
C. The standard error of the sample proportion estimate (SEest) is the same as the standard error of the sample proportion (SE) calculated in part B. Hence, the standard error of the sample proportion estimate is also approximately 0.041 (rounded to three decimal places).
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find the value of X?
Answer:
x = 58
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
90 = 32+x
Subtract 32 from each side
90-32 = x
58 =x
Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Accounting 83 Management 68 Marketing 85 Economics 64 Total 300 Has there been any significant change in the number of students in each major between the last school year and this school year?
Answer:
There has been no significant change in the number of students in each major between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: There has been no change in the number of students.
Hₐ: There has been a significant change in the number of students.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
Here,
[tex]O_{i}[/tex] = Observed frequencies
[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.
The chi-square test statistic value is, 1.662.
The degrees of freedom is:
df = 4 - 1 = 4 - 1 = 3
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]
*Use a Chi-square table.
The p-value is 0.645.
The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.
Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
15x - y = - 126
Step-by-step explanation:
will make it simple and short
first we need to find the slope (m) first in order to get the equation
given: (-8,6) (-9,-9)
y2 - y1 -9 - 6
Slope = m = ----------- = ------------------ = 15
-x2 - x1 -9 - (-8)
so the equation of the line using point (-8,6) and slope 15 is y - 6 = 15( x + 8)
y - 6 = 15x + 120
using the form equation Ax + By = C, 15x - y = -120-6
therefore... 15x - y = - 126 is the answer
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The z-score is [tex]z = 0.6[/tex]
The percentile is [tex]p(Z < 0.6) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
The data value is 0.6 standard deviations above the mean i.e [tex]x = \mu + 0.6 \sigma[/tex]
Where [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation
Generally the z-score is mathematically represented as
[tex]z = \frac{x - \mu }{\sigma }[/tex]
=> [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]
=> [tex]z = 0.6[/tex]
The percentile is obtained from the z-table and the value is
[tex]p(Z < 0.6) = 0.7257[/tex]
=> [tex]p(Z < 0.6) = 72.57\%[/tex]
Find the solution of the system of equations.
2x – 10y = -28
-10x + 10y = -20
GbA
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 10y = - 28 → (1)
- 10x + 10y = - 20 → (2)
Adding (1) and (2) term by term eliminates the term in y, that is
- 8x = - 48 ( divide both sides by - 8 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
2(6) - 10y = - 28
12 - 10y = - 28 ( subtract 12 from both sides )
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Solution is (6, 4 )
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - 1/2x
B.
y = 1/2x
C.
y = 2x
D.
y = -6x
E.
y = 6x
F.
y = 3x
Answer:
y=-6x
Step-by-step explanation:
An aluminum bar 4 feet long weighs 24 pounds. What is the weight of a similar bar that is 3 feet 3 inches long? WILL MARK BL
Answer:
19.5 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.5 pounds
Answer:
19.50 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.50 pounds
Write an equation showing the relationship between the lengths of the three sides of a right triangle.
Answer:
Below
Step-by-step explanation:
First triangle)
This triangle is a right one so we will apply the pythagorian theorem.
● 25 is the hypotenus
● 25^2 = b^2 + 24^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Seconde triangle)
Again it's a right triangle
x is the hypotenus.
● x^2 = 12^2 +5^2
● 12^2 = x^2-5^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
This is a right triangle
AC is the hypotenus.
● AC^2 = BC^2 + BA^2
Notice that: BC = BE+EC and BA=BD+DA
● AC^2 = (BE+EC)^2 + (BD+DA)^2
Answer: 2) b = 7 3) x = [tex]\sqrt{119}[/tex]
Step-by-step explanation:
Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²
2) b² + 24² = 25²
b² + 576 = 625
b² = 49
[tex]\sqrt{b^2}=\sqrt{49}[/tex]
b = 7
3) 5² + x² = 12²
25 + x² = 144
x² = 119
[tex]\sqrt{x^2}=\sqrt{119}[/tex]
[tex]x=\sqrt{119}[/tex]
A caplet contains 325 mg of medication. How many caplets contain 975 mg of medication?
Answer:
3 capletsStep-by-step explanation:
Given 1 caplet = 325 mg of medication, to calculate the number of caplet 975mg of medication will contain, we will follow the steps below;
Let 1 caplet = 325 mg of medication
x caplet = 975 mg of medication
Cross multiply
325 * x = 1 * 975
325x = 975
Divide both sides by 325
325x/325 = 975/325
x = 3
Hence 3 caplets contains 975 mg of medication.
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Answer options given in picture
Michael can skateboard 100 feet in 5.4 seconds. Which choice below shows how fast Micheal is going miles per 1 hour? Remember that since you are using multiplication to make conversions, you need to set up the units diagonal from each other in order to cancel.
any unrelated answer will be reported
Answer:
A
Step-by-step explanation:
Which cross-sectional shapes do you find the most surprising? Which shapes do you find the least surprising? Explain why.
Answer:
I was surprised that a plane parallel to the vertical axis creates a rectangular cross-section. I guess I was expecting to always see a circle or a circular shape in the cross-section, not purely straight edges as seen in a rectangle.
Step-by-step explanation:
edmentum answer
Answer:
The circles were the least surprising because the base of the cone is a circle. The curves that look like bent rods were the most surprising because I have not seen geometric figures like those before.
Step-by-step explanation:
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2]
Answer:
Yes , it satisfies the hypothesis and we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Step-by-step explanation:
Given that:
[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]
which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]
Differentiating the function with respect to x is;
f(x) = 8x - 3
Using the Mean value theorem to see if the function satisfies it, we have:
[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]
since the polynomial function is differentiated in [0,2]
[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]
[tex]8c -3 = \dfrac{10}{2}[/tex]
8c -3 = 5
8c = 5+3
8c = 8
c = 8/8
c = 1
Therefore, we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
The algebraic expression for the product of five and the cube of a number decreased by 40
Answer:
5a³ - 40
Step-by-step:
The algebraic expression is:
5a³ - 40
Help with a problem again please
Answer:
9x³ + 27x²
Step-by-step explanation:
What the question is asking is to multiply f(x) and g(x) together:
Step 1: Write out expression
(fg)(x) = 3x²(3x + 9)
Step 2: Distribute
(fg)(x) = 9x³ + 27x²
Answer:
[tex]\huge\boxed{Option \ 3 : (fg)(x) = 9x^3+27x^2}[/tex]
Step-by-step explanation:
[tex]f(x) = 3x+9\\g(x) = 3x^2[/tex]
Multiplying both
[tex](fg)(x) = (3x+9)(3x^2)\\(fg)(x) = 9x^3+27x^2[/tex]
A project has an initial cost of $40,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to the nearest cent.
Answer:
50k
Step-by-step explanation:
2/5(10c -35) (the 35 is negative)
Answer:
The simplified form is 2 (c - 7).
Step-by-step explanation:
The expression to be solved is:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
Simplify the expression as follows:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
[tex]=[\frac{2}{5}\times 10c]-[\frac{2}{5}\times 35]\\\\=[2\times 2c]-[2\times 7]\\\\=4c-14\\\\=2(c-7)[/tex]
Thus, the simplified form is 2 (c - 7).
To paint his apartment, Alex but 6 gallons of paint to cover 1440 ft.². What is the ratio of square feet to gallons of paint?
Answer & Step-by-step explanation:
The ratio of square feet to gallons of paint:
[tex]1440:6[/tex]
This can also be written as:
[tex]\frac{1440}{6}[/tex]
This fraction can be simplified by dividing the numerator and denominator by 6:
[tex]\frac{1440}{6}=\frac{240}{1}[/tex]
So, the ratio of square feet to gallons of paint is:
1 gallon for every 240 ft².
:Done
A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
Use the quadratic function to predict f(x) if x equals 2. f(x) = −3x2 + 180x − 285
Answer:
if x = 2
f(x) = -3x^2 + 180x -285
f(x) = -3*2*2 + 180*2 -285
f(x) = -12 + 360 -285
f (x) = 63
Step-by-step explanation:
Please Help me with this Click to select the following graphic figure. A square circumscribed about a circle:
The answer would be the first image.
Step-by-step explanation:
From context, it appears that to be circumscribed is to be drawn about; thus the square circumscribed about the circle is the first graph.
Answer:
The first image which is a circle in a square
12. 12 ounces is roughly the same as
O A. 340 grams.
B. 356 grams.
O C. 400 grams.
O D. 120 grams.
Mark for review (Will be highlighted on the movin
Answer:
A. 340 grams
Step-by-step explanation:
My brain
1. What is the difference between an exponential growth and exponential decay? 2. What is an example equation for expoential growth and an example equation for exponential decay?
Answer: see below
Step-by-step explanation:
The standard form of an exponential equation is: y = a(b)ˣ where
a is the initial valueb is the rateGrowth:
Exponential growth is where the final value (y) is greater than the initial value (a).
An example would be the spreading of a rumor:
You tell 1 person (a = 1) who then tells 2 people each minute (b = 2). How many people will they have spread the rumor to after 5 minutes (x = 5)?
y = 1(2)⁵
= 32
Decay:
Exponential decay is where the final value (y) is less than the initial value (a).
An example would be the decrease of bacteria in a person:
A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2). How many bacteria will the person have after 2 hours (x = 2)?
[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]
Simplify 70 +(-30)+2+(-9)+0.3+(-0.1)=[70+(-30)] +[2+(-9)]+[0.3+(-0.1)]
Answer:
Step-by-step explanation:
When you add the left side of the equation, you get 33.2 because 70-30 is 40, 40+2 is 42, 42-9 is 33, 33+0.3 is 33.03, 33.3-0.1 is 33.2.
When you add the right side of the equation, you get 33.2, because they are the same problem but on side has brackets.
Hope this helps you.
how many feet are in 53 yards, 2 feet? enter only the number. Do not include units
There are 161 feet are in 53 yards, 2 feet.
What is unit conversion?
Unit conversion is the process of changing a quantity's measurement between various units, frequently using multiplicative conversion factors.
As we know that;
1 yard = 3 feet
53 yards = 3 ×53 feet
53 yards = 159 feet
53 yards, 2 feet = 159 feet + 2 feet
53 yards, 2 feet = 161 feet
Hence, there are 161 feet in 53 yards, 2 feet.
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