Answer:
0.2207
Step-by-step explanation:
Here, we want to find the probability that the sample mean is greater than 25.
What we use here is the z-scores statistic
Mathematically;
z-score = (x-mean)/SD/√n
From the question;
x = 65, mean = 63, SD = 13 and n = 25
Plugging these values in the z-score equation, we have
Z-score = (65-63)/13/√25 = 2/13/5 = 0.77
So the probability we want to calculate is ;
P(z > 0.77)
This can be obtained from the standard normal distribution table
Thus;
P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p
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]
A triangle has vertices at (-4,-6),(3,3),(7,2). Rounded to two decimal places, which of the following is closest aporoximation of the perimeter of the triangle
Answer:
Perimeter= 29.12 unit
Step-by-step explanation:
Perimeter of the triangle is the length of the three sides if the triangle summef up together
Let's calculate the length of each side.
For (-4,-6),(3,3)
Length= √((3+4)²+(3+6)²)
Length= √((7)²+(9)²)
Length= √(49+81)
Length= √130
Length= 11.40
For (-4,-6),(7,2)
Length= √((7+4)²+(2+6)²)
Length= √((11)²+(8)²)
Length= √(121+64)
Length= √185
Length= 13.60
For (3,3),(7,2)
Length=√( (7-3)²+(2-3)²)
Length= √((4)²+(-1)²)
Length= √(16+1)
Length= √17
Length= 4.12
Perimeter= 4.12+13.60+11.40
Perimeter= 29.12 unit
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]
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]
3.85∙47.3+52.7∙3.85 PLSSSSS HELP
Answer:
385
Step-by-step explanation:
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
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:
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]
Jamal has two investments, one in Company A, and another in Company B. Jamal purchased 300 shares in Company A at $1.45 per share. Since purchasing the shares, the price per share increased to $1.65 per share, after which Jamal decided to sell, realizing a profit. At the same time, Jamal purchased 200 shares in Company B at $1.20 per share. Since purchasing the shares, the share price fell to $1.10 per share, after which Jamal decided to sell the shares, suffering a loss. Calculate the total profit that Jamal received from his two investments.
Answer:
$20
Step-by-step explanation:
Company A:
Buy 300 shares at $1.45 per share.
Sell 300 shares at $1.65 per share.
Profit: ($1.65 - $1.45) * 300 = $60
Company B:
Buy 200 shares at $1.20 per share.
Sell 200 shares at $1.10 per share.
Loss: ($1.20 - $1.10) * 200 = $20
Net profit:
$40 - $20 = $20
Answer:
Step-by-step explanation:
Profit on Company A =$(1.65−1.45)×300=$60.
Loss on Company B =$(1.20−1.10)×200=$20.
Therefore the total profit Jamal achieved was $60−$20=$40.
solve the following equations for x (3x-6)=18
Answer:
x = 8
Step-by-step explanation:
Hello!
What we do to one side of the equation we have to do to the other side.
3x - 6 = 18
Add 6 to both sides
3x = 24
Divide both sides by 3
x = 8
The answer is 8
Hope this helps!
Answer:
x=8
Step-by-step explanation:
(3x-6)=18
Add 6 to each side
(3x-6+6)=18+6
3x= 24
Divide by 3
3x/3 = 24/3
x = 8
Find the area of the shaded regions.
Answer:
7 pi cm^2 or approximately 21.98 cm^2
Step-by-step explanation:
First find the area of the large circle
A = pi r^2
A = pi 3^2
A = 9 pi
Then find the area of the small unshaded circle
A = pi r^2
A = pi (1)^2
A = pi
There are two of these circles
pi+ pi = 2 pi
Subtract the unshaded circles from the large circle
9pi - 2 pi
7 pi
If we approximate pi as 3.14
7(3.14) =21.98 cm^2
Answer:
[tex]\boxed{\sf 7\pi \ cm^2 \ or \ 21.99 \ cm^2 }[/tex]
Step-by-step explanation:
[tex]\sf Find \ the \ area \ of \ the \ two \ smaller \ circles.[/tex]
[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]
[tex]\sf r=radius \ of \ circle[/tex]
[tex]\sf There \ are \ two \ circles, \ so \ multiply \ the \ value \ by \ 2.[/tex]
[tex](2) \pi (1)^2[/tex]
[tex]2\pi[/tex]
[tex]\sf Find \ the \ area \ of \ the \ larger \ circle.[/tex]
[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]
[tex]\sf r=radius \ of \ circle[/tex]
[tex]\pi (3)^2[/tex]
[tex]9\pi[/tex]
[tex]\sf Subtract \ the \ areas \ of \ the \ two \ circles \ from \ the \ area \ of \ the \ larger \ circle.[/tex]
[tex]9\pi -2\pi[/tex]
[tex]7\pi[/tex]
PLEASE ANSWER ASAP!!!
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:
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
5(y–3.8)=4.7(y–4) help help
Answer:
y = 2/3 or 0.667Step-by-step explanation:
5(y–3.8)=4.7(y–4)
Expand the terms in the bracket
That's
5y - 19 = 4.7y - 18.8
Group like terms
5y - 4.7y = 19 - 18.8
0.3y = 0.2
Divide both sides by 0.3
We have the final answer as
y = 2/3 or 0.667Hope this helps you
A department store offers two promotions. Promotion A says, "Buy one pair of shoes, get the second pair for half the price." Promotion B says, "Buy one pair of shoes, get $10 off the second pair." Jane wants to buy two pairs of shoes that cost $30 each. She can only use one of the promotions, A or B. Jane decides to use the promotion that will save her the most money. How many dollars does Jane save by picking one promotion over the other? (For example, if Jane spends $150 on her purchase by using one promotion and $100 on her purchase by using the other promotion, she saves $150-100=50$ dollars by using the second promotion over the first.)
Answer:
$5
Step-by-step explanation:
Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.
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
Find the value of angle X. x = 40 x = 55 x = 109 x = 130 I will mark as Brainliest
Answer:
130 degree
Step-by-step explanation:
Interior angles of the triangle:
81, 49, (180-x)
and by sum of all angles of triangle is 180 degree,
therefore,
81 + 49 + 180 - x = 180
x = 130 degree
g natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that natasha is one of the leaders
Answer:
3,654 different ways.Step-by-step explanation:
If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).
Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.
29C3 = 29!/(29-3)!3!
29C3 = 29!/(26!)!3!
29C3 = 29*28*27*26!/26!3*2
29C3 = 29*28*27/6
29C3 = 3,654 different ways.
This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders
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).
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
Alex wants to sew a pillow in the shape below. How many square yards of fabric are needed to sew the pillow? Fabric is only sold in increments of ¼ yard.
The shape is missing, so i have attached it.
Answer:
2.6
Step-by-step explanation:
From the image attached, the diameter of the inner semi - circle is 0.5 yards while the length of each side of the pillow is 0.2 yards.
Thus, for us to find the length of the seam which is along the edges of the pillow, we will calculate the perimeter of the outer semicircle, then add the perimeter of the inner semicircle and also add the sides too.
Now, due to the fact that the length of the sides of the pillow are 0.2 yards each, the diameter of the outer circle would be;
0.5 + 0.2 + 0.2 = 0.9 yards. So, the perimeter of the outer semicircle is,
P0 = πd/2 = π × 0.9/2 =0.45π yds
The perimeter of the inner semicircle would be given as;
PI = πd/2 = π × 0.5/2 =0.25π yds.
Thus, we can calculate the total perimeter of the pillow as;
PT = P0 + PI + 0.2 + 0.2
PT = 0.45π + 0.25π + 0.2 + 0.2
PT ≈ 2.6 yards
Alex will need 2.6 yds
Answer:
0.5
Step-by-step explanation:
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
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:
The difference of two trinomials is x2 − 10x + 2. If one of the trinomials is 3x2 − 11x − 4, then which expression could be the other trinomial? 2x2 − x − 2 2x2 + x + 6 4x2 + 21x + 6 4x2 − 21x – 2
Answer: [tex]4x^2-21x-2[/tex] .
Step-by-step explanation:
Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].
Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])
[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]
Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .
Best Buy is currently selling the latest model of the iPad
Pro for $549.99. Since you are an employee there, you
receive a 5% discount. How much will the iPad Pro cost
you if you use your employee discount (before taxes).
Answer:
$522.49
Step-by-step explanation: 549.99*.05=27.50 (discount)
549.99-27.50=$522.49
Answer:
$522.49
Step-by-step explanation:
First, find the discount amount. You can do this by multiplying the original cost by the discount amount. A little trick for remembering to multiply instead of divide is to think "five percent of the original amount"
5% = 0.05
549.99 ⋅ 0.05 = 27.4995
That means the discount amount is $27.50
Subtract the discount amount from the original price
$549.99 - $27.50 = $522.49
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]
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
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.
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]
