By using the remainder theorem we found that ( x - 5 ) is the factor of function f(x) = x³ – 5x² + 7x – 35.
What is factorization?Factorization is defined as splitting the polynomial into its most simplified form. This factor satisfies the polynomials from which it is extracted.
The factorization by using the Remainder theorem.
x - 5 ) x³ – 5x² + 7x – 35.( x ² + 7
x³ - 5x²
______________
00 7x - 35
7x - 35
-------------------------
00
Here the function is completely divided by the factor x - 5 therefore
by using the remainder theorem we found that ( x - 5 ) is the factor of function f(x) = x³ – 5x² + 7x – 35.
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Jordan and Taylor are collecting canned foods for the homeless. They hope to collect 10 cans per day to reach their goal. They have already collected 120 cans. If the
function for this problem is f(c) = 10r+120, determine how many cans Jordan and Taylor will have collected after 8 days.
Answer:
200 cans.
Step-by-step explanation:
f(c)=10r + 120
Put t=8 into it
T(c) = 10 x 8 + 120
=200 cans
(Use substitution method)
n studying the sampling distribution of the mean, you were asked to list all the different possible samples from a small population and then find the mean of each of them. Consider the following: Personal phone calls received in the last three days by a new employee were 2, 4, and 7. Assume that samples of size 2 are randomly selected with replacement from this population of three values. What different samples could be chosen? What would be their sample means?
The Total outcome with replacement will be given by ,3² = 9, the mean of the samples will be 2 , 4.5 , 3 , 7 , 4
What is Mean ?Mean predicts the central tendency of a data set , It is determined by the ratio of sum of all the numbers to the total numbers in the data set.
On the basis of given data
The number given is 2,4,7
Size of the sample = 2 with replacement
The Total outcome with replacement will be given by
3² = 9
Possible outcome can be
2,2 2,4 2,7 4,4 4,2 4,7 7,7 7,2 7,4
The sample mean can be calculated as
(a+b)/2
(2+2)/2 = 2
similarly the mean of the samples will be 2 , 4.5 , 3 , 7 , 4
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Mrs. Hilt owns a house on a lot shaped like a rectangle. The perimeter
of the lot is 60 feet. What is the length and the width of the lot?
Answer:
2l + 2w = 60
Step-by-step explanation:
I am not able to tackle this question. Somebody please help me out
The minimum load at which a certain kind of iron wire breaks can be supposed to define a random variable normally distributed with expected value 80N and standard deviation 3N. Find the probability that such a wire will break when the load is (a) 74N
(b)89N
The wire breaks if the load [tex]X[/tex] exceeds some amount. So what you're asked to do is find [tex]P(X\ge74)[/tex] and [tex]P(X\ge89)[/tex].
In either case, transform [tex]X[/tex] to the random variable [tex]Z[/tex] that's normally distributed with expected value 0 and standard deviation 1.
[tex]P(X\ge74) = P\left(\dfrac{X-80}3 \ge \dfrac{74-80}3\right) \\ = P(Z \ge -2) \\ = 1-P(Z < -2) \approx 0.9773[/tex]
[tex]P(X\ge89) = P\left(\dfrac{X-80}3 \ge \dfrac{89-80}3\right) \\= P(Z \ge 3) \\= 1 - P(Z < 3) \approx 0.0013[/tex]
Express cos A as a fraction in simplest terms.
Answer:
See below
Step-by-step explanation:
Here is one way
cos^2 + sin^2 = 1
cos^2 = 1 - sin^2
For angle A cos^2 = 1 - (10/26)^2
cos ^2 = 1 - 100/676
= 576/676
cos A = 24/26 = 12/13
Another way would be to use the Pythagorean theorem to find length of AB .... then cos A = length AB / 26
Help me with this question please and thank you!! :)
Question 1
The complement of set B is all the elements in S but that are not in B, which is [tex]\{2, 4, 5, 9, 10, 11, 12, 13, 14, 17, 19\}[/tex].
We want to find the intersection of set A and the complement of set B, which is the set of all elements that both sets contain.
This is {2, 9, 10, 12}, meaning there are 4 elements.
Question 2
Following a similar logic as the last problem, the complement of set A is [tex]\{1,3,4,5,6,7,11,13,14,15,17,18,19\}[/tex].
Therefore, the desired set is [tex]\{1,3,6,7,15,18\}[/tex], and thus there are 6 elements.
for f(x)-4x+1 and g(x)-x^2-5, find (g/f) (x)
Answer:
A.
Step-by-step explanation:
let me know if you want an explanation :))
Answer:
A
Step-by-step explanation:
Which of the following probabilities is the greatest for a standard normal distribution? P (negative 1.5 less-than-or-equal-to z less-than-or-equal-to negative 0.5) P (negative 0.5 less-than-or-equal-to z less-than-or-equal-to 0.5) P (0.5 less-than-or-equal-to z less-than-or-equal-to 1.5) P (1.5 less-than-or-equal-to z less-than-or-equal-to 2.5)
The probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have a statement:
Which of the following probabilities is the greatest for a standard normal distribution:
The options are:
P(-1.5 ≤ z ≤ -0.5)
P(-0.5 ≤ z ≤ 0.5)
P(0.5 ≤ z ≤ 1.5)
P(1.5 ≤ z ≤ 2.5)
As we know from the normal distribution curve we can find the probability between the range given. At Z=0, the chance is 50-50.
From the Z-curve:
P(-1.5 ≤ z ≤ -0.5) = 9.2% + 15% = 24.2%
P(-0.5 ≤ z ≤ 0.5) = 19.1% + 19.1% = 38.2%
P(0.5 ≤ z ≤ 1.5) = 15% + 9.2% = 24.2%
P(1.5 ≤ z ≤ 2.5) = 4.4% + 1.7% = 6.1%
Thus, the probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.
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Answer:
B) P (-0.5 <= z <= 0.5)
Step-by-step explanation:
If everything in a store is 20% off, and the discounted price of an item is $18.00, what is
the regular price?
The regular price is $22.5 if everything in a store is 20% off, and the discounted price of an item is $18.00
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
If everything in a store is 20% off, and the discounted price of an item is $18.00
Let's suppose the regular price is x
(100-20)% of x = 18
80x/100 = 18
x = $22.5
Thus, the regular price is $22.5 if everything in a store is 20% off, and the discounted price of an item is $18.00
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also can someone check this too? just want to make sure i got the the first part right before proceed further
Answer:
the answers are all right
Inverse Function: One to one function...Help needed! 15 pts for your help!
Answer:
Step-by-step explanation:
hello :
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the expressions given in words with their values when m = 6. 2 15 42 3 21
The matching is done below
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
1) 3 is the difference of 2 times d minus 3.
As, 2*d - 3
=2*3 - 3
=6 - 3
= 3
2) 4 is 4 added to the difference of d minus 3.
or, 4 + (d - 3)
or, 4 + (3 - 3)
or, 4 + 0 = 4
3) 0 is the difference of d minus 3 divided by 2.
(d - 3)/2
= (3 - 3)/2
= 0/2
= 0
4) 2 is the quotient of 12 divided by the difference of 3 times d minus 3.
12/(3d - 3)
=12/(3*3 - 3)
=12/(9 - 3)
=12/6
= 2
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What is the weighted average cost of capital (WACC) for ABC Limited which has the following capital structure? $5m of equity with a cost of equity of 15%; $2m of mezzanine finance with a cost of 9.5%; $1m of senior debt with a cost of debt of 7%.
Answer:
the answer is 13.73 %
Find the least number which when divided by 12, 18 and 20 leaves no reminder.
Answer:
180
Step-by-step explanation:
Find the LCM of 12, 18, and 20
[tex]12 = 2 \times 2 \times 3[/tex]
[tex]18 = 2 \times 3 \times 3[/tex]
[tex]20 = 2 \times 2 \times 5[/tex]
LCM = 2 × 2 × 3 × 3 × 5 = 180
What is the formula for finding the area of abc?
The formula for finding the area of the triangle ΔABC will be half of the product of the base and height. Then the formula is A = 1/2 x BC x AD.
What is the area of the triangle?The area of the triangle is given as
A = 1/2 x B x H
Where B is the base and H is the height of the triangle.
The triangle is given below,
We have
B = BC
H = AD
Then we have
A = 1/2 x BC x AD
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Please help!
38 [tex]\frac{22}{75}[/tex] + 3 [tex]\frac{11}{15}[/tex] = ?
The value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]
How to add the fractions?The summation expression is given as:
[tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex]
Rewrite as:
[tex]38 + 3 + \frac{22}{75} + \frac{11}{15}[/tex]
Evaluate the sum and take LCM
[tex]41 + \frac{22 + 5 * 11}{75}[/tex]
Evaluate the sum
[tex]41 + \frac{77}{75}[/tex]
Express as mixed number
[tex]41 + 1\frac{2}{75}[/tex]
Add
[tex]42\frac{2}{75}[/tex]
Hence, the value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]
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need help with this question please
∠ A = 132°
Step-by-step explanation:
∠ A + ∠C = 180° (Angle sum of cyclic quadrilateral)
∠ A = 180° - ∠ C = 180° - 48°
∠ A = 132°
Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2X - 3Y = 6 at X = 3
The slope-intercept expression for the line is, y=2x-6
The slope-intercept formula is the one we require for this issue.
y = mx + b is the expression that provides the answer.
where 'm' is the equation's scale's slope and 'b' is the y-intercept, or the point on the y-axis in which the line intersects, respectively.
Since, the x-intercept of the line 2x-3y=6 is (3, 0), we desire the following line's expression, which has a slope of 2, to pass over the position (3,0).
Use the formula y=mx +b, x=3, y=0 to get 'b'.
Hence,
0 = 2(3) + b
⇒ b= -6,
∴The expression for the line is y= 2x-6.
This line will cross at x=3 and 2x-3y=6.
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A coin is tossed, and a die is rolled. What is the probability that the outcome is a head or an even number?
Answer: When a coin is tossed and a die is rolled the probability of getting a head or an even number is = 3/4
Step-by-step explanation:
probability : The ratio of the favorable outcome to the total outcomes is gives the probability.
So for the given case all possible outcomes are = 12(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)
total no of outcomes when there is head on coin are = 6(1,H),(2,H),(3,H),(4,H),(5,H),(6,H)
Total no of outcomes when there is even on dice are = 3(2,T),(4,T),(6,T)
So the total number of favorable outcomes are:6+3 = 9
Total outcomes = 12Therefore the probability is given by 9/12 = 3/4
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Answer: The probability of getting a head or an even number is = 3/4
What is probability?It is the measure of how likely an event or outcome is. Different events have different probabilities!For the given case: Possible outcomes are(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)
So, no. of possible outcomes 12
No. of coin outcomes (when it's head) = 6(1,H),(2,H),(3,H),(4,H),(5,H),(6,H)
No of dice outcomes (when it's even) = 3(2,T),(4,T),(6,T)
So the total number of favourable outcomes are:6+3 = 9
Total outcomes = 12
Probability = [tex]\frac{No. of favorable outcomes}{total outcomes}[/tex]
Probability for this case is = [tex]\frac{9}{12} =\frac{3}{4}[/tex]
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This is the full question
Answer:
< $0 --------------$35------ $50>
Step-by-step explanation:
I see it's still the same, the maximum discount can be put off is still $50
and you can find that out by discount 30% off 50 to get $35 :)
< $0 --------------$35------ $50>
A manufacturer of pacemakers wants the standard deviation of the lifetimes of the batteries to be less than 1.8 months. A sample of 20 batteries had a standard deviation of 1.6 months. Assume the variable is normally distributed. Find the 95% confidence interval of the standard deviation of the batteries. Based on this answer, do you feel that 1.8 months is a reasonable estimate?
Answer:
Look down my answer↓:
Step-by-step explanation:
The Candle Factory is producing a new candle. It has a radius of 3 inches and a height of 5 inches. How much wax is needed to make the candle? Use 3.14 for Pi. Round to the nearest whole cubic inch.
A cylinder with a radius of 3 inches and height of 5 inches.
Recall the formulas S A = 2 pi r squared + 2 pi r h and V = pi r squared h.
141 cubic inches
236 cubic inches
443 cubic inches
565 cubic inches
Answer:
141 cubic inches
Step-by-step explanation:
The candle can be modeled as a cylinder.
To find how much wax is needed to make the candle, calculate the volume of the cylinder.
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 3 inh = 5 inπ = 3.14Substitute the given values into the formula and solve for V:
[tex]\implies \sf V=3.14 \cdot 3^2 \cdot 5[/tex]
[tex]\implies \sf V=3.14 \cdot 9 \cdot 5[/tex]
[tex]\implies \sf V=28.26 \cdot 5[/tex]
[tex]\implies \sf V=141.3\:in^3[/tex]
Therefore, the amount of wax needed to make the candle is 141 cubic inches (nearest whole cubic inch).
A regular polygon has n sides.
How many pairs of parallel sides does the polygon have if:
a) n is odd?
b) n is even?
The number of pairs of parallel sides of the polygon have no parallel sides if n is odd and n/2 pair of parallel sides if n is even.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
A regular polygon has n sides.
Then the number of pairs of parallel sides of the polygon will be
IF n is odd, then none of the sides are parallel.
If n is even, then the number of pair of parallel sides will be n / 2.
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find arc length
x=t^(3)-2t
y=t^(2)-3
Answer:
Step-by-step explanation:
How much is Bob's net salary for the week? Question 32
Answer:
A. $152.00
Step-by-step explanation:
I'm 99% sure the net salary is just the 220 (gross salary) minus everything else taken away which is (42 + 7 + 15 + 4) = 68. 220 - 68 = 152 so Bob's net salary would be 152
Select "Yes" or "No" to indicate whether the ordered pair is on the graph of the function f(x)=−25^x+1.
Among all the three ordered pairs no one lies on the graph of the function f(x)=[tex]-25^{x} +1[/tex].
Given The value of a function f(x)=[tex]-25^{x} +1[/tex]
If we want to check whether it will lie on the graph of a function or not then we have to just put those points in the function ,if the function satisfies means they lie on that graph otherwise not.
Taking first ordered pair :(1,625)
value of x is 1 and value of y is 625.
we have to put in the function so
625=-[tex]25^{1}+1[/tex]
625 is not equal to -24 so it does not satisfy.
Taking second ordered pair :(0,-25)
-25=-25 raise to power 0 +1
-25 is not equal to 1 so it does not satisfy.
Taking third ordered pair: (-1,-1)
-1=-1/25+1
-1 is not equal to 24/25 so it does not satisfy.
Hence among all the ordered pairs none will lie on line of the given function.
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Choose True or False, (T or F). Grouped data is a data that has not been organized into intervals.
The statement "Grouped data is a data that has not been organized into intervals" is false.
Data presented in class intervals, such as 0-20, 20-40, and so on, is referred to as "grouped data."
Ungrouped data is information presented as individual values or integers, such as 15, 63, 34, 20, 25, and so on.
Assume we have a set of data with values between 0 and 50, such as 2, 17, 0, 1, 8, 19, 43, 2, 1, 32, and so on. In this situation, we may divide the data into categories like 0-10, 10-20,...,40-50. The data in this case are simply grouped.
Hence, the statement "Grouped data is a data that has not been organized into intervals" is false.
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John needs to put the set of numbers below in ascending order.
3, -1, √5, 13, -11
Which number should John write first?
A. -1
B. -11
C. √5
D. 13
A linear function on a coordinate plane passes through (minus 2, 3), (minus 1, 0), (0, minus 3), and (1, minus 6)
Which equation describes the line graphed above?
A.
B.
C.
D.
The equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The options are missing.
The options are:
A) y = 3x - 3
B) y = -3x + 3
C) y = 3x + 3
D) y = -3x - 3
From the points [tex]\left(-2,3\right)[/tex] and [tex]\left(-1,0\right)[/tex]:
[tex]\rm y\ =\ \dfrac{3}{-1+2}\left(x+1\right)[/tex]
y = 3(x + 1)
y = 3x + 3
Thus, the equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
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Question is in attached file
The rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
The distance traveled by passenger train = 245 miles
The distance traveled by freight train = 245 miles
The time takes for both trains is the same.
Let's suppose the rate of the passenger train is x and the rate of the freight train is y;
As we know,
Distance = speed×time
245/x = 200/y
200x = 245y
200x - 245y = 0 ..(1)
x = 15 + y ..(2)
Equations (1) and (2) represent the situation.
After solving equations (1) and (2):
[tex]\rm x=\dfrac{245}{3}= 81.67\\\\\\\:y=\dfrac{200}{3}=66.67[/tex]
Thus, the rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.
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