The membership of the gym after 7 years is 1385 .
What is a function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable ). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
Given: The function : M(x)= 180x + 125
where x is the number of years so in this case we have to find the value of M when x= 7 years
Thus the given function on substituting the value becomes
M (7)= 180× 7 + 125
= 1385.
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Find the slope m and y-intercept b. (If an answer is undefined, enter UNDEFINED. If an answer does not exist, enter DNE.)
x = −9
m =
b =
Answer: undefined, DNE
Step-by-step explanation:
This is a vertical line, so there is an undefined slope and no y-intercept.
There is no y-intercept because the line does not pass through the origin.May I please get help with this. For I have tried multiple times but still could not get the correct answers for them or even plot it on the graph 90 degrees clockwise
To rotate the figure 90 degrees clockwise about a point, every point (x, y) will rotate to (y, -x):
[tex](x,y)\to(y,-x)[/tex]The vertices of the triangle have the following coordinates:
[tex]\begin{gathered} 1=(-5,-1) \\ 2=(-1,-2) \\ 3=(-3,-4) \end{gathered}[/tex]Applying the transformation rule, we have the new coordinates to be:
[tex]\begin{gathered} 1\to(-1,-(-5))=(-1,5) \\ 2\to(-2,-(-1))=(-2,1) \\ 3\to(-4,-(-3))=(-4,3) \end{gathered}[/tex]The transformed image is shown below (the black triangle):
provide the correct reason for the statement in line 4. (please help)
The property that completes the proof is the transitive property
How to determine the statement that represents the reason in the proof?From the question, we have the following parameters
The point C is the midpoint of AE
BC = CD
The above implies that
AC = CE
And it also means that:
The line segment BC and the line segment CD have equal lengths
According to the transitive property of equation, we have:
If A = B and B = C, then A = C
This can also be represented as
If A + B = C + D and C + D = E + F, then A + B = E + F
Using the above as a guide, we have (in step 3)
AB + BC = AC
CD + DE = CE
This implies that
AB + BC = CD + DE
Hence, the statement that represents the reason 4 in the proof is (b) transitive property
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Can somebody help me with this please ?
The correct answer is option d, output = 6 - input using coordinate geometry.
What is coordinate geometry?In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
From the graph, we can see that the coordinates have the values
For x = 1, y = 5
For x = 2, y = 4
For x = 3, y = 3
For x = 4, y = 2
Hence, we can conclude that the output (y) = 6 - input (x)
The correct option is (d) output = 6 - input.
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A rental car agency charges $240.00 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $477.50
Answer: 950
Step-by-step explanation:
$477.50 - $240.00 = 237.50
$237.50 / $0.25 = 950
What is the percent change if you paid $1.87 per gallon on February 6th and $1.80 per gallon on February 17th?
The percent change formula is:
[tex]\frac{\text{new price - previous price}}{\text{previous price}}\cdot100[/tex]In this case, the percent change is:
[tex]\frac{1.8-1.87}{1.87}\cdot100=-3.74\text{ \%}[/tex]f(x) = 8x + 1, g(x) = 4x - 2
Find (fg)(x).
f(g(x)) for the given equation f(x)=8x+1 and g(x)=4x-2 is 32x-15 using substitution method of solving the equation.
What is equation?An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. It is a formula that expresses the connection between two expressions on each side of a sign.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
given,
f(x)=8x+1
g(x)=4x-2
f(g(x))=8(4x-2)+1
=32x-16+1
f(g(x))=32x-15
Hence, this is required f(g(x)) for the given two equations.
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I’m struggling on question number 16, me and friend are getting VERY different answers and I would like to get a good grade in this class!
Solution:
Given a sphere of diameter, d, 2.5ft.
To find the volume, V, of the sphere, the formula to apply is
[tex]V=\frac{4}{3}\pi r^3[/tex]Where, the radius, r, is
[tex]\begin{gathered} r=\frac{d}{2}=\frac{2.5}{2}=1.25ft \\ r=1.25ft \end{gathered}[/tex]Substitute for r into the formula to find the volume of a sphere above
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\times\pi\times1.25^3 \\ V=8.18123\text{ ft}^3 \\ V=8.2\text{ ft}^3\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]Hence, the volume, V, of the given sphere is 8.2 ft³ (the nearest tenth)
I need help with this problem
)
2) So, let's begin with the lower-left product of matrices:
[tex]\begin{gathered} \begin{pmatrix}-2 & 12 \\ -1 & -3\end{pmatrix}\times\begin{pmatrix}2 & 1 \\ 4 & 2\end{pmatrix}= \\ \begin{pmatrix}\left(-2\right)\cdot \:2+12\cdot \:4&\left(-2\right)\cdot \:1+12\cdot \:2\\ \left(-1\right)\cdot \:2+\left(-3\right)\cdot \:4&\left(-1\right)\cdot \:1+\left(-3\right)\cdot \:2\end{pmatrix} \\ \begin{pmatrix}44&22\\ -14&-7\end{pmatrix} \end{gathered}[/tex]Now for the next pair of matrices in the middle:
[tex]\begin{gathered} \begin{pmatrix}2 & 0 \\ 1 & 0\end{pmatrix}\times\begin{pmatrix}3 & -1 \\ 2 & 2\end{pmatrix}= \\ \begin{pmatrix}2\cdot \:3+0\cdot \:2&2\left(-1\right)+0\cdot \:2\\ 1\cdot \:3+0\cdot \:2&1\cdot \left(-1\right)+0\cdot \:2\end{pmatrix} \\ \begin{pmatrix}6&-2\\ 3&-1\end{pmatrix} \end{gathered}[/tex]Notice that each row is multiplied by each correspondent column.
And finally, the pair on the lower-right:
[tex]\begin{gathered} \begin{pmatrix}5&-2\\ \:\:\:4\:&-3\end{pmatrix}\times \begin{pmatrix}2&-1\\ \:\:3&1\end{pmatrix} \\ \begin{pmatrix}5\cdot \:2+\left(-2\right)\cdot \:3&5\left(-1\right)+\left(-2\right)\cdot \:1\\ 4\cdot \:2+\left(-3\right)\cdot \:3&4\left(-1\right)+\left(-3\right)\cdot \:1\end{pmatrix} \\ \begin{pmatrix}4&-7\\ -1&-7\end{pmatrix} \end{gathered}[/tex]) Thus, the se are theanswers .
a(1)= -13
a(n)= a(n-1)+4
Find the 2nd term in the sequence
The second term of the arithmetic sequence is:
a₂= -9
How to find the second term in the sequence?Here we have an arithmetic sequence, such the the recursive formula is:
aₙ = aₙ₋₁ + 4
So to get each term, we need to add 4 to the previous one.
We know that the first term is:
a₁ = -13
Then the second term will be:
a₂ = a₁ + 4 = -13 + 4 = -9
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A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 1 or less, the lot passes inspection. Suppose 10% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection? Round your answer to four decimal places
can someone help me on this
Answer:
The best estimate for the correlation coefficient is .85.
Find the area of a triangle bounded by the
y
axis, the line
f
(
x
)
=
4
−
1
5
x
, and the line perpendicular to
f
(
x
)
that passes through the origin.
The area of a triangle bounded by the region will be 11.95 sq. units.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that,
y = f(x) = 7- (4/5)x
Slope,m = -4/5
The slope of the perpendicular lines is,
[tex]\rm m_p = \frac{-1}{\dfrac{-4}{5}} \\\\ m_ p = \dfrc{5}{4}[/tex]
The equation of the perpendicular line passing through the origin is
[tex]\rm y = \frac{5}{4} x[/tex]
The equation can be written as,
[tex]\rm \frac{5}{4} x = 7 - \frac{4}{5} x \\\\ 25 x = 140 - 16 x \\\\ 41x = 140 \\\\ x = \dfrac{140}{41} \\\\ y = \frac{175}{41}[/tex]
As a result, the y-intercept of the line is,
[tex]\rm y =7- \dfrac{4}{5}x \\\\ y= 7[/tex]
The triangle is bounded by the points (0,0), (0,7), and (140/41, 175/41)
The area of the triangle is,
[tex]\rm A= \frac{1}{2} \times 7 \times \dfrac{140}{141} \\\\ A = 11.95 \ sq. unit[/tex]
Thus, the area of a triangle bounded by the region will be 11.95 sq. unit.
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In the game, your score grew by 200 points each time you scored. Two expressions below represent your echoes after 12 hits. Find both.
A) 200 + 200 + - - - + 200 +200
—————————————————
12times
B) 200 ⚫️ 200 ⚫️ - - - ⚫️ 200 ⚫️ 200
—————————————————
12times
C) 200 ⚫️ 12
D) 200 + 12
Answer: A and C
Sample Answer: Multiplication is a short way to write repeated addition. So 200 •12 means the same as 200 + 200 + . . . + 200.
Answer:
b
Step-by-step explanation:
Gina is driving 76 miles to her brother's house. If she stops for gas after driving 34 miles, how many miles does she have to go before she gets to her brother's house?
Answer:
42
Step-by-step explanation:
76-34
Write the component form of the vector.
Answer:
C , D
Step-by-step explanation:
The component form of a vector is given as < x, y >, where x describes how far right or left a vector is going and y describes how far up or down a vector is going.
The component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.
To write the component form of a vector, we simply list its components, which are the numerical values that represent the vector's magnitude and direction in each dimension. In this case, we have vector C with components C<1, 5> and vector D with components D<8, 2>.
The components of a vector represent its position or displacement along the coordinate axes. In a two-dimensional Cartesian coordinate system, the first component represents the displacement along the x-axis (horizontal direction), and the second component represents the displacement along the y-axis (vertical direction).
For vector C, the component form is written as <1, 5>, where the first component is 1 and the second component is 5. This means that vector C has a displacement of 1 unit in the x-direction and 5 units in the y-direction.
Similarly, for vector D, the component form is <8, 2>, indicating a displacement of 8 units in the x-direction and 2 units in the y-direction.
Therefore, the component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.
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Which of the following is equivalent to −2(4x + 8y) − 5(3q + 6p)?
−8x + 8y − 15q + 6p
−8x + 16y − 15q + 30p
−8x − 16y − 15q − 30p
−10(4x + 8y − 3q + 6p)
Answer:
-8x + 16y -15q - 30p
Step-by-step explanation:
your just expanding brackets here
Answer: -8x - 16y - 15q - 30p Is the correct answer
I hope this helps!
A rectangular tabletop has an area of 28 1/8 sqaure feet length of 6 1/4 feet what is the width of the tabletop
If a rectangular tabletop has an area of [tex]28\frac{1}{8}[/tex] square feet and the length of [tex]6\frac{1}{4}[/tex] feet, then the width of the tabletop is [tex]4\frac{1}{2}[/tex] feet
The area of the tabletop = [tex]28\frac{1}{8}[/tex] square feet
Convert the mixed fraction to simple fraction
[tex]28\frac{1}{8}[/tex] square feet = 225/8 square feet
The length of the tabletop = [tex]6\frac{1}{4}[/tex] feet
Convert the mixed fraction to simple fraction
[tex]6\frac{1}{4}[/tex] feet = 25/4 feet
Area of the rectangle = Length × width
Width of the rectangle = Area of the rectangle ÷ Length of the rectangle
Substitute the values in the equation
Width of the rectangle = 225/8 ÷ 25/4
= 225/8 × 4/25
= 9/2 feet
Convert the simple fraction to mixed fraction
9/2 feet = [tex]4\frac{1}{2}[/tex] feet
Hence, if a rectangular tabletop has an area of [tex]28\frac{1}{8}[/tex] square feet and the length of [tex]6\frac{1}{4}[/tex] feet, then the width of the tabletop is [tex]4\frac{1}{2}[/tex] feet
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The number of pairs of shoes owned by a sample of seven students are given below. Match the measure to its value.
3, 3, 5, 9, 12, 13, 15
1. range
2. variance
3. standard deviation
12
5
25
According to the solving the given data the values of :
Range = 12
Variance= 25
Standard deviation= 5
What does "variance in statistics" mean?Data points' deviations from the mean are quantified by their variance. Layman defines variance as the degree to which a set of data (numbers) deviates from the mean (average) value. Finding the predicted difference between the deviation from the actual value and the variation.
What do you mean by range?In statistics, range is the distinction between the most and least values in a set. Mathematics' interval, also known as range, is a collection of real numbers that contains all values that fall between any two other values.
According to the given data:Given data: 3, 3, 5, 9, 12, 13, 15
Range = Highest value - lowest value
= 15 - 3
= 12
Mean of the given data:
xi = 3, 3, 5, 9, 12, 13, 15
n = 7
S² = ∑(xi - x)²/(n - 1)
= (30.25 + 30.25 + .25+ 12.25 + 20.25 + 42.25 + 12.25)/6
= 147.75/6
= 24.6
= 25
Finding the standard deviation:
√S² = 25
S = 5
According to the solving the given data the values of :
Range = 12
Variance= 25
Standard deviation= 5
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The point Q lies on the segment PR.
Find the coordinates of Q so that PQ is
Check
17/0 of PR.
P(-3,4)
Coordinates of Q: D
Q (?, ?)
R (24,-32)
X
Save For Later
Submit
Answer:
Step-by-step explanation:
it would be 42,32 i know
help meeeeeeeeee
12 Answer:
Evaluate the expression: 8-6+4
13 Answer:
Evaluate the expression: 16÷(4-2)-3
14 Answer:
Check whether the given number is a solution of the equation:
3x + 5 = 17; x=2
a. solution is correct
b. solution is incorrect
15 Answer:
Check whether the given number is a solution of the equation:
4y - 7 = 3y - 4; y=3
a. solution is correct
b. solution is incorrect
16 Answer:
Check whether the given number is a solution of the inequality:
2m - 3 < 4; 2
a. number is a solution
b. number is not a solution
17 Answer:
Check whether the given number is a solution of the inequality:
5 + 2n ≥ 12; 0
a. number is a solution
b. number is not a solution
Answer:
Step-by-step explanation:
13) 8 - 6 + 4 = 2 + 4 = 6
14) 16÷(4-2)-3 = 16÷2 - 3 = 8 - 3 = 5
15) 3x + 5 = 17
3x = 17 - 5
3x = 12
x = 4 ≠ 2
b. solution is incorrect
16)4y - 7 = 3y - 4
4y - 3y = -4 + 7
y = 3
a. solution is correct
17) 2m - 3 < 4
2m < 4 + 3
2m < 7
m < 3.5
2 < 2.5, so a. number is a solution
18 ) 5 + 2n ≥ 12
2n ≥ 12 - 5
2n ≥ 7
n ≥ 3.5
0 is not greater than equal to 3.5, so b. number is not a solution
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
If one order is selected, find the probability of getting an order that is not accurate or is from Restaurant C. Are the events of selecting an order that is not accurate and selecting an order from Restaurant C disjoint events?
The probability is 0.334 and the events are not disjoint events
How to determine the probability?The table of values represents the given parameters
The probability to calculate is given as
The probability of getting an order that is not accurate or is from Restaurant C
This can be represented as
P(Not accurate or Restaurant C)
This is calculated as
P(Not accurate or Restaurant C) = [n(Not accurate) + n(Restaurant C) - (Not accurate and Restaurant C)]/Total
So, we have
P(Not accurate or Restaurant C) = (37 + 52 + 34 + 19 +237 + 34 - 34)/(330 + 276 + 237 + 150 + 37 + 52 + 34 + 19)
Evaluate the sum and the difference
P(Not accurate or Restaurant C) = 379/1135
Evaluate the quotient
P(Not accurate or Restaurant C) = 0.334
Lastly, the events of selecting an order that is not accurate and selecting an order from Restaurant C are not disjoint events
This is so because it is possible to select an order from restaurant C that is not accurate
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If AC=19 and BC=7, find the length of AB.
Find the area of a parallelogram that is 6m height 7m length
Answer:
Area (A) = 42m²
Step-by-step explanation:
A = b·h = 6·7 = 42m²
Please help with the following question:
Using the combination formula, it is found that:
a) There are 210 distinct ways to choose the problems.
b) The probability is of 0.1667 = 16.67%.
c) The probability is of 0.3333 = 33.33%.
What is the combination formula?[tex]C_{n,x}[/tex] gives the number of different combinations of x objects from a set of n elements, according by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The order in which the problems are chosen is not important, which is the reason for the use of the combination formula in this problem.
4 problems are chosen from a set of 10, hence the number of ways to choose the problems is given by:
[tex]C_{10,4} = \frac{10!}{4!6!} = 210[/tex]
The number of ways to choose 4 problems that she can solve is:
[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]
Hence the probability is:
p = 35/210 = 0.1667 = 16.67%.
For item c, the desired outcomes are as follows:
0 problems is not possible, as she knows 7 out of 10 and 4 will be chosen.1 problem: 7 x C(3,3) = 7.2 problems: C(7,2) x C(3,2) = 21 x 3 = 63.Hence the probability is:
p = (7 + 63)/210 = 70/210 = 0.3333.
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Find the volume of this rectangular pyramid Be sure to include the correct unit in your answer
Okay, here we have this:
Considering the provided rectangular pyramid, we are going to calculate the requested volume, so we obtain the following:
Then, we are going to use the following formula to find the volume of this rectangular pyramid:
V=(abH)/3
Replacing:
V=(abH)/3
V=(5cm*6cm*7cm)/3
V=(210cm^3)/3
V=70 cm^3
Finally we obtain that the volume of the rectangular prism is 70 cm^3.
determine the volume of each rectangular prism.. round to the nearest tenth if necessary
The volume of a rectangular prism is given by the formula:
[tex]V=\text{length}\times\text{width}\times\text{height}[/tex]Given the length is 7 cm
Width is 3 cm
Height is 3 cm
Substituting into formula, we find the volume:
[tex]\begin{gathered} V=7\times3\times3 \\ V=63\operatorname{cm}^3 \end{gathered}[/tex](-35) divided by 7 =?
Answer:
-5
Step-by-step explanation:
Answer: -5
Step-by-step explanation: -35 divided by 7 is -5
Nidia cut a rectangle into 2 pieces as shown below.
12 ft
20 ft
20 ft
12 ft
She put the pieces together to form a parallelogram. What is the area of the parallelogram?
The area of the parallelogram is 240 feet.
What is area of parallelogram?A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.
A quadrilateral's interior angles add up to 360 degrees.
The area of a parallelogram can thus be written as :
Area = Base × Height
In this diagram it is given that the Base = 20 feet and the height = 12 feet
Thus the area can be obtained by simply multiplying these two dimensions
So area = 20 × 12 = 240 feet .
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The balance on a credit card, that charges a 15.5%
APR interest rate, over a 1 month period is given in
the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily
balance, for this card over this 1 month period?
finance charge = $ [?]
Round to the nearest hundredth.
Enter
4
Finance charge = $93.00
What is finance charge of credit card?The interest you'll pay on a loan is defined as a finance charge, and it's most commonly used in the context of credit card debt. A financing fee is computed by taking your annual percentage rate, or APR, the amount you owe, and the time period into account.
Given that,
Interest rate = 15.5%
Date: 1-3 (3 days)
Average daily balance = amount paid × days
= $200 × 3 = $600
Date: 4-20 (17 days)
Average daily balance = amount paid × days
= $300 × 17 = $5100
Date: 21-30 (10 days)
Average daily balance = amount paid × days
= $150 × 10 = $1500
So, total average daily balance for the month
= $(600+5100+1500)
= $7200
Now, the finance charge = $7200 × (15.5÷12)
= $93.00
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