Answer:
50 + 5x^2 + 4x.
Step-by-step explanation:
To find the sum of the expressions, we need to simplify each expression first and then add them up.
10 + 3x represents the first expression.
25 - 4x + 2x^2 represents the second expression. By simplifying this expression, we get 25 + 2x^2 - 4x.
3x^2 - 5x represents the third expression.
-x^2 + 2x + 15 represents the fourth expression.
Adding all four expressions gives us:
10 + 3x + 25 + 2x^2 - 4x + 3x^2 - 5x - x^2 + 2x + 15
By combining like terms, we get:
10 + 5x^2 + 4x + 25 + 15
The final simplified sum is:
50 + 5x^2 + 4x.
Hercules crawled on fifth of a mile in a one tenth of an hour. find the rate in miles per hour
In linear equation, 2 miles per hour is the rate in miles per hour .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Divide the distance by the time.
(1/5 miles) / (1/10 hour)
= 10(1/5) miles per hour
= 2 miles per hour
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The entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056. How many adults and how many children were there in this group?.
The number of adults and children in the group were 64 and 36 respectively by using an algebraic equation.
It is given that the entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056.
Let the number of adults in the group = x
number of adults in the group = y
Total number of people paid an entry fee = 100
So the equation becomes : x + y = 100
or x = 100 - y
Cost for adult ticket = $12
Cost for child ticket = $8
Total entry fee paid = $1,056
Second equation = 12x + 8y = 1056
putting value of x from equation 1
12(100 - y) + 8y = 1056
1200 - 12y + 8y = 1056
4y = 144
y = 36
x = 100 - 36 = 64
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Given right triangle ABC with altitude
BD drawn to hypotenuse AC. If
AC 36 and DC = 9, what is the length
of BC?
=
C
9
D
36
X
A
B
Can someone please helppp
The measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangles; ∆ABC with hypotenuse = 45 and adjacent = BC, the triangle ∆ADC with hypotenuse = BC and adjacent = 9 with the angle C we can solve for BC as follows:
for ∆ABC;
cosC = 9/BC {adjacent/hypotenuse}
for ∆ADC;
cosC = BC/45 {adjacent/hypotenuse}
9/BC = BC/45
BC² = 9 × 45 {cross multiplication}
BC² = 405
BC = √405 {take square root of both sides}
BC = 20.1246
Therefore, the measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
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Which of the following is something you would not expect to see on a basic loan application?
On solving the provided question, we can say that expression is - doctor’s name and address, EDG 2020
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
expression is -
doctor’s name and address
EDG 2020
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The correct question is -
Which of the following is something you would not expect to see on a basic loan application?
a. employer's name and address
b. doctor's name and address
C. annual or monthly income
d. current monthly rent or mortgage payment
Please select the best answer from the choices provided
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
Answer:
the IQR is the best measure which equals 16
Step-by-step explanation:
the 2nd option is not correct because, while the range is 45, there are only two out of eleven data items above 45, which is not representative of the majority of the data
the 3rd option is incorrect because the IQR does not equal 45, it's 16
the 4th option is incorrect because the range does not equal 16, it's 45
What is the actual length which is represented by 3.2cm on a scale drawing with scale 1cm to 4cm
Answer: 12.8 cm
Step-by-step explanation:
Multiply 3.2 by the scale of 4 to get 12.8.
A verbal description of a linear function g is given. Express the function g in the form
g(x) = ax + b.
The linear function g has rate of change −12 and initial value 100.
g(x) =
G is a linear function with a rate of change of -12 and an initial value of 100. Its equation is: g = -12x + 100.
What is a linear function?Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.
What does the described linear function look like?As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.
Since f(x) = axe + b is the typical slope-intercept form of a linear function,
an is the slope (rate of change), and b is the y-intercept (initial value).
g = -12x + 100 is the necessary linear function, which is what has been presented.
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In an isosceles triangle, one angle is 24° greater than each of the other two equal angles.
Find the measure of all three angles.
The two smaller angles are each _____
The two smaller angles are 39 degrees each. The other angle is 106
How to solve for the anglesThe measure of the angles would be found using the formula
2*x + 24 = 180
This is because the sum of angles that are in a triangle is = 180
the two equal angles are x + x = 2x
the other angle is 24 greater than 2x
2x + 24 = 180
2x = 180 - 24
2x = 156
x = 78
eaxh of the two equal angles are 78 degrees
while the other angle is 78 + 24 = 106
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Rowan was collecting seashells she collects 4 more than three times the number of seashells Maribel collects if Maribel collects X seashells select the expression of represents the number of seashells Rowan collects
Answer:
Rowan collects
3x + 4
Step-by-step explanation:
Maribel collects x sea shells.
Rowan collects 4 more (this is the +4)
than 3 times Maribels (this is the 3x)
Maribel = x
Rowan = 3x + 4
Answer:
its actually 4x + 3
Step-by-step explanation:
Find HP
Round to the nearest whole meter
Check the picture below.
Make sure your calculator is in Degree mode.
From the picture, find the value of the pawn in each of the following problems, and write the check
Answer:
6) x = 6
7) x = 4
8) x = 4
9) x = 6
10) x = 6
Step-by-step explanation:
This is based on Dr. Henry Borenson's method of using pawns to explain algebraic equations. Frankl I find using variables more intuitive
Let each pawn represent an x in the equations
6.
x + 8 = 10 + 4
x = 10 + 4 - 8
x = 14 - 8 = 6
7.
x + x = 4 + x
2x = 4 + x
2x - x = 4
x = 4
8.
x + x + x + 2 = 7 + 7
3x + 2 = 14
3x = 14 - 2
3x = 12
x = 12/3
x = 4
9.
2x + 4 = x + 10
2x - x = 10 - 4
x = 6
10
3x = x + 10 + 2
3x = x + 12
3x - x = 12
2x = 12
x = 6
In a running race, you covered 3000 m. The ratio of distance covered by walking to running is 2:13. How many meters did you walk?
Answer:
400 m walking
Step-by-step explanation:
sum the parts of the ratio , 2 + 13 = 15 parts
divide the distance covered by 15 to find the value of one part of the ratio.
3000 m ÷ 15 = 200 m
then
2 parts = 2 × 200m 400 m
400 m covered by walking
2. Determine the area of each composite figure below.
Answer:
[tex]6\pi[/tex]
Step-by-step explanation:
There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.
Area of a Circle:The area of a circle can be calculated using the formula: [tex]A=\pi r^2[/tex] where "r" is the radius, equal to half the diameter.
Since we're dealing with the semi-circles, we can just divide this area by two to get: [tex]A=\frac{\pi r^2}{2}[/tex]
Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.
So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: [tex]A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi[/tex]
One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.
So now let's calculate the area of the inner semi-circle: [tex]A=\frac{\pi (2)^2}{2}=2\pi[/tex]
Now let's just subtract the areas: [tex]8\pi - 2\pi = 6\pi[/tex], so the area is 6 pi
Consider a linear function where
F(-10)=64 and f(15)=54
Find the equation
The equation is f(x) = -0.4x + 60. The solution has been obtained by using slope - intercept form.
What is slope-intercept form?
The graph of the equation y = mx + b is a line with a slope of m and a y-intercept of b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.
We are given that f(-10) = 64 and f(15) = 54.
So, we get the points as (-10 , 64) and (15 , 54)
Using the slope intercept form, we get
Slope(m) = (54 - 64)/(15 + 10)
Slope(m) = -0.4
We know that y = mx + b
For calculating b. we will put in the values
⇒64 = -0.4(-10) + b
⇒64 = 4 + b
⇒b = 60
From this we get the equation as
f(x) = -0.4x + 60
Hence, the equation is f(x) = -0.4x + 60.
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If a graph of y=-9x + 11 were changed to a graph of y=-9x+14, how would the y-intercept change? OA. The y-intercept of the new graph would shift up 3 units. B. More information is needed to determine the change. C. The y-intercept would remain the same. D. The y-intercept of the new graph would shift down 3 units.
Answer:
Step-by-step explanation:
The y-intercept of a linear equation in slope-intercept form, y = mx + b, represents the point at which the line crosses the y-axis. In this form, "m" represents the slope of the line and "b" represents the y-intercept.
If we have a graph of y = -9x + 11, the y-intercept can be found by setting x equal to 0 and solving for y:
y = -9x + 11
y = -9 * 0 + 11
y = 11
So, the y-intercept of the original graph is (0, 11).
Now, if we have a graph of y = -9x + 14, the y-intercept can be found in the same way:
y = -9x + 14
y = -9 * 0 + 14
y = 14
So, the y-intercept of the new graph is (0, 14).
Comparing the y-intercepts of the two graphs, we can see that the y-intercept of the new graph has shifted up by 3 units, from (0, 11) to (0, 14).
Therefore, the correct answer is A: The y-intercept of the new graph would shift up 3 units.
Z-score with the area of 0.0054if the area is halfway between two entry’s use the z score halfway between the corresponding z scores
Write the equation of the transformation of g(x) = 4* by shifting up 2, shifting right 5, reflecting over the
X -axis, and then horizontally compressing by a factor of 5.
f(x) =
The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
g(x) = 4ˣ
The function is shifting up 2 and shifting right 5. Then the function is given as,
g(x) = 4⁽ˣ⁺⁵⁾ + 2
The function after reflecting over the x-axis is given as,
- g(x) = 4⁽ˣ⁺⁵⁾ + 2
g(x) = - 4⁽ˣ⁺⁵⁾ - 2
And then horizontally compressing by a factor of 5. Then the function is given as,
f(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2
The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.
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Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.8 degrees.
Low Temperature
(circle◦F)
40minus−44
45minus−49
50minus−54
55minus−59
60minus−64
Frequency
22
55
1212
77
11
The mean of the frequency distribution is____ degrees. (Round to the nearest tenth as needed.)
Which of the following best describes the relationship between the computed mean and the actual mean?
A. The computed mean is close to the actual mean because the difference between the means is less than 5%.
B. The computed mean is not close to the actual mean because the difference between the means is less than 5%.
C. The computed mean is not close to the actual mean because the difference between the means is more than 5%.
D. The computed mean is close to the actual mean because the difference between the means is more than 5%.
The mean of the frequency distribution is 52 degrees. and option A is carrect . A) The computed mean is close to the actual mean because the difference between the means is less than 5%
First, we calculate the class mid-points (x); This is the mean of the class intervals.
For 40 - 44, x = (40 + 44)/2 = 42. This is applied to all other classes.
40 −44 = 42
45 −49 = 47
50 −54 = 52
55 −59 =57
64 −64 = 62
So:
x 42 47 52 57 62
f 22 55 1212 77 11
mean = ∑f(x)/∑f
= (42*22+47*55+52*1212+57*77+62*11)/(22+55+1212+77+11)
= 71604/1377
=52
actual mean = 51.8
and now mean = 52
percentage difference = ((52-51.8)/51.8)*100
= 0.3861 percentage
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in a recent survey of 500 people,it was found that 2800 read Concord and 2300 read guardian while 400 read both papers. How many read neither
300 people read neither of the papers.
How to find how many read neither?Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental theory in mathematics and can be used as a foundation for all other areas of mathematics.
Total population n(ξ) = 5000
Number of people reading Concord, n(C) = 2800
Number of people reading Guardian, n(G) = 2300
Number of people reading both = n(C ∩ G)] = 400
Number of people reading any of the newspaper = n(C ∪ G)] = n(C) + n(G) - n(C ∩ G) = 2800 + 2300 - 400 = 4700.
Number of people reading none of them is equal to = Total population - Number of people reading any of the newspaper = 5000 - 4700 = 300
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The inequalities 3x<1 and 6x<2 are equivalent inequalities. Write another inequality that is equivalent to 3x<1 and 6x<2.
One inequality that is equivalent to 3x<1 and 6x<2 is 3x<1/2.
To see why this is true, we can divide both sides of the second inequality by 2, which gives 3x<1/3. However, we want an inequality that is equivalent to both 3x<1 and 6x<2, so we need to find a common solution.
Notice that if 3x<1, then x<1/3. And if 6x<2, then x<1/3 as well (since 1/3 is less than 2/6). Therefore, the intersection of the solutions for these two inequalities is x<1/3.
But we want an inequality in the form of 3x<a, where a is some constant. To find this value, we need to solve for x in the intersection of the two solutions:
x<1/3
Multiplying both sides by 3 gives:
3x<1
So we can choose a=1/2, which gives us the final inequality:
3x<1/2
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A baseball coach purchased bats and batting helmets. The coach purchased 19 items in all. Each bat cost $18.25 and each batting helmet cost $24.50. If the coach spent a total of $396.75, how many bats did the coach purchase?
Answer:
11 bat and 8 helmets.
Step-by-step explanation:
Let x = the number of bats
Let y = the number of batting helmets
x + y = 19 Rewrite as y = 19 - x
18.25x + 24.50y = 369.75 Multiply by 100
1825x + 2450y = 36975 Substitute 19 - x for y
1825x + 2450(19 -x) = 39675 Distribute the 2450
1825x + 46550 - 2450x = 39675 combine like terms
-625x + 46550 = 39675 subtract 46550 from both sides
-625x = -6875 Divide both sides by -625
x = 11
He bought 11 bats
x + y = 19 Substitute 11 for x to solve for y
11 + y = 19 Subtract 11 from both sides
y = 8
He bought 8 helmets.
-17
ng
2
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Chapter 3: Probability (Add and Mult)
Score: 22.75/38 26/38 answered
Question 29
>
A bag contains 7 red marbles, 5 white marbles, and 6 blue marbles. You draw 3 marbles out at random,
without replacement. Find the following probabilities and round to 4 decimal places.
a. The probability that all the marbles are red is
b. The probability that none of the marbles are red is
a. The probability that all the marbles are red is calculated as follows:
(7 choose 3) / (18 choose 3) = (35 / (816)) = 0.0429
So, the probability that all the marbles are red is 0.0429, rounded to 4 decimal places.
b. The probability that none of the marbles are red is calculated as follows:
(12 choose 3) / (18 choose 3) = (220 / 816) = 0.2696
So, the probability that none of the marbles are red is 0.2696, rounded to 4 decimal places.
You randomly pull a marble from a bag of marbles. The bag has 2 red
marbles, 1 pink marble, 1 green marble, and 5 speckled marbles,
What is the probability of not drawing a green marble? Write your
answer as a decimal rounded to the nearest hundredth.
A
Answer:
0.89
Step-by-step explanation:
As there is 1 green marble out of 9 total marbles, there's a 1 in 9 chance of selecting the green marble. This means that its complement would be the probability of NOT selecting the green marble would be 8/9, or about 0.89
Answer:0.89
Step-by-step explanation:
Help please! Which of the following tables represents a relation that is a function? Explained answer please
A
B
C
D
Answer:
Step-by-step explanation:
THE ANSWER TO YOUR QUESTION IS C.
3 1/5+n=9 which can be used to solve this equation
Find the circumference of a circle with a diameter of 8 inches
Answer:
B
Step-by-step explanation:
c=d*π
c=8*π
c=25.1 inches
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The median home value in Pennsylvania and Nevada (adjusted for inflation) are shown below.
Year Pennsylvania Nevada
1950 42400 53700
2000 97000 142000
If we assume that the house values are changing linearly,
a) In which state have home values increased at a higher rate?
Nevada
Correct
b) If these trends were to continue, what would be the median home value in Pennsylvania in 2010?
$
c) If we assume the linear trend existed before 1950 and continues after 2000, the two states' median house values will be (or were) equal in what year? (The answer might be absurd)
The year
According to the given statement Nevada's property prices have grown more rapidly , median home value 148,880 and median house values will be 15.6.
What does the median in housing mean?The selling price of the middle property in a list of properties listed by highest sale price through lowest over a predetermined time period is the median house price. Thus, if 71 homes were sold, the median home price would correspond to the sale price of the 36th home.
Rate of change for Pennsylvania [tex]= (97000 - 42400) / (2000 - 1950) = 1092[/tex]
Rate of change for Nevada [tex]= (142000 - 53700) / (2000 - 1950) = 1816[/tex]
As a result, Nevada's property prices have grown more rapidly.
b) Median home value of Pennsylvania in 2010[tex]= 42400 + 1092 * (2010 - 1950) = $148,880[/tex]
c) Pennsylvania[tex]= 42400 + 1092x[/tex]
Nevada[tex]= 53700 + 1816x[/tex]
[tex]42400 + 1092x = 53700 + 1816x\\724x = 11300\\x = 15.6[/tex]
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A chest has a length of 0.8 m, a width of 0.5 m
and a height of 0.6 m. What is the volume of the
chest?
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a standard deviation of 0.04. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.04, Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. P KQ 0 Oso X X a Р S 00 020
The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.
The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.
Mathematically, the null and alternative hypotheses can be expressed as follows:
H0: σ = 0.04
Ha: σ ≠ 0.04
where σ represents the standard deviation of the number of accidents per day.
The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.
2.63 divied by 0.5 standard way
Answer: 5.26
Step-by-step explanation:
Answer:
= 0.190
Solution:
Change the divisor 2.63 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
50 ÷ 263 = 0.190
and therefore:
0.5 ÷ 2.63 = 0.190
Both calculated to 3 decimal places.
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