Tom’ mot recent book earned 10*4 time a much money a hi firt book. then The amount that Tom’s most recent book earn is 10^7.
How to illustrate the exponent?
The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.
The total amount of the recent book will be:
= 10⁴ × 10³
= 10^(4 + 3)
= 10^7
The amount is 10^7.
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Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?.
The correct option is (0, 0), is the only viable solutions for the number of books and total weight of the books.
Explain the term viable solutions?Any answer that makes sense in the context of a question is deemed to be a viable one.For the stated question;
b represents the number of books.w represents the total weight of books, in ounces.Weight of each book = 6 ouncesWe may create an equation that describes the relationship between the number of books with their net weight if b stands in for the total weight. The formula can be
b = 6w
The very first two pairs are eliminated since you never order less than a certain quantity of books. Additionally, you don't buy half a book, which eliminates the final pair.Therefore, the number of books as well as the total weight will be represented by the (0,0) ordered pair that solves the above equation.
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The complete question is-
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces? (–3, –18) (–0.5, –3) (0, 0) (0.5, 3)
Answer:
C. 0,0
Step-by-step explanation:
Which expression is equivalent to 63.56 (–81.47)? 63.56 – 81.47 63.56 81.47 –63.56 – 81.47 –63.56 81.47
The expression 63.56 (-81.47) is equivalent to 63.56 - 81.47.
Option (A) is correct.
What is subtraction?
Subtraction is an arithmetic operation that involves finding the difference between two numbers. In mathematics, subtraction is represented by the minus sign (-).
To find the value of 63.56 (-81.47), we need to perform the arithmetic operation of subtraction. In this case, 63.56 is the minuend and -81.47 is the subtrahend.
The expression 63.56 (-81.47) is equivalent to 63.56 + (-81.47), which is equal to
The result of this subtraction is -17.91.
Hence, the expression 63.56 (-81.47) is equivalent to 63.56 - 81.47.
Option (A) is correct.
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Find the point, m, that is two-sevenths of the distance from a(-9, 2) to b(-2, -12).
(-7,-2) is the point which is two-sevenths of the distance from a(-9, 2) to b(-2, -12).
since the unknown point m divides line joining a(-9,2) and b(-2,-12) in a given ratio of 2:5 as it is given one point is at distance of 2/7 of distance between point a and b so, the other point must be at a distance of 5/7 and hence the ratio in which it divides itself is 2:5
a_______________m_________________________b
2 : 5
in the above figure it is shown clearly that m divides line joining point a and point b in the ratio of 2:5
let (x,y) be cordinate of point m
[tex](x_1 , y_1)[/tex] be the point a
[tex](x_2 , y_2)[/tex] be point b
m:n =2:5
m=2 ,n=5
so applying section formula
x= [tex]\frac{mx_2+nx_1}{m+n}[/tex]
=> x = (2* -2 + 5 *-9) / (5+ 2)
=> x = - 49/7 = -7
y= [tex]\frac{my_2+ny_1}{m+n}[/tex]
=> y = (2* -12+5 *2)/(5+2)
=> y = -2
so the point m is (-7,-2) is the required answer of the question
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FILL IN THE BLANK. a(n) ____________ difference is due to some systematic influence and not due to chance.
The correct option is (a) significant.
a(n) significant difference is due to some systematic influence and not due to chance.
Significant: Having or likely to have influence or effect : important. a significant piece of legislation also of a noticeably or measurably large amount. a significant number of layoffs.
Insignificant: small or unimportant
null: Lacking meaning or having no value
serendipitous: come upon or found by accident
As per the question the suitable answer is option (a).
Therefore, the correct answer is Significant
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A(n) significant difference is due to some systematic influence and not due to chance. Choose one answer.
a. significant b. insignificant c. null d. serendipitous
The function S(d)= 86log d +112 relates the speed of wind, S, in miles per hour, near the centre of a tornado to the distance the tornado travels, d, in miles. Estimate the rate at which the speed of the wind at the centre of the tornado is changing the moment it has traveled its 50th mile.
The rate at which the speed of the wind changes at the 50th mile is 258.114 miles per hour
How to estimate the rate at which the speed of the windFrom the question, we have the following parameters that can be used in our computation:
Function: S(d) = 86log d + 112
Express the above function properly
So, we have the following representation
S(d) = 86log(d) + 112
From the question, we have:
Distance = 50th mile.
This means that
d = 50
Substitute the known values in the above equation, so, we have the following representation
S(50) = 86log(50) + 112
Evaluate the logarithm
So, we have the following representation
S(50) = 86 * 1.699 + 112
Evaluate the products
S(50) = 146.114 + 112
Lastly, we have
S(50) = 258.114
Hence, the speed is 258.114 miles per hour
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Pls help I also need to classify the polynomial by the # of terms
The 12+5x² Leading Coefficient is 5, the [tex]2p^{2} +4p^{4} -5[/tex] Leading Coefficient is 4. and The -5y³ Leading Coefficient is -5
What is polynomial function?
A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.
Solution:
1) 12+5x²
Standard form: 5x²+12 Degree: 2Leading Coefficient: 52) [tex]2p^{2} +4p^{4} -5[/tex]
Standard form: [tex]4p^{4} +2p^{2}-5[/tex] Degree: 2+4=6Leading Coefficient: 43) -5y³
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(-4/9) * 11/12
plss answer fastttttttttttttttttttttttttttttttttt!!!!!
plsssssssssss
Step-by-step explanation:
a/b × c/d = (a×b)/(c×d)
so,
-4/9 × 11/12 = (-4×11) / (9×12) = -44/108 = -11/27
A driver travels 120 miles, stops, and then travels ¼ of the distance she has already driven. After stopping again, the driver travels ⅔ of the distance she has already traveled. Now, the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. How many miles does the driver still have to travel?
Let x be the number of miles the driver still has to travel.
The driver traveled 120 + 120/4 + 120/42/3 = 120 + 30 + 40 = 190 miles.
So the remaining distance is x + 190 = 55 + 1 2/3 * x
Multiplying both sides by 3/2 gives 3/2x + 3/2190 = 3/255 + 3/2*x + x
This simplifies to x = 190.
Therefore, the driver still has to travel 190 miles.
help me solve this please
Answer:
20.50 < 13 + .75n; 10 < n
Step-by-step explanation:
First let us set up 2 equations to represent how much these payment methods are giving per hour:
f(n) = 20.50
g(n) = 13 + .75n
We want to find where f(n) < g(n):
20.50 < 13 + .75n → subtract 13
7.50 < .75n → divide by .75
10 < n
Thus, we would need to produce more than 10 units per hour to get the second option to be more profitable
(4,4), (5,4), (6,4), (7,4), (8,4) B. (6,9), (7,19), (8,29), (8,39), (9,49) C. (7,33), (8,30), (9,27), (10,24), (11,21) D. (4,4), (5,6), (6,8), (6,10), (7,12) Which of thee relation are function?
As per the rule of function, the relation (4,4), (5,6), (6,8), (6,10), (7,12) is a function.
The term relation in math referred as the relationship between two or more set of values.
Here we have to find in which of the given relation is a function.
As we all know that the function is a relation which describes that there should be only one output for each input or we can say that a special kind of relation (a set of ordered pairs),
Therefore, the rule of the function states that every X-value should be associated with only one y-value is called a function.
As per this rule we have identified the following relation is one that said to be the function
=> (4,4), (5,6), (6,8), (6,10), (7,12)
Therefore, option (D) is correct.
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The sum of two numbers is 62, and their difference is
12. What are the numbers?
Answer:
25 and 37
Step-by-step explanation:
x+y=62
y-x=12
+x. +x
y=12+x
x+(12+x)=62
2x+12=62
-12. -12
2x=50
/2. /2
x=25
25 is one of the numbers
y-25=12
+25 +25
y=37
hopes this helps
the amount of time taken by each of 10 students in a class to complete an exam is an example of what type of data?
the amount of time taken by each of 10 students in a class to complete an exam is an example of quantitative data.
Quantitative data is numerical data which can be used to measure and quantify a certain phenomenon. In this example, the amount of time taken by each of the 10 students in a class to complete an exam is a numerical value, and it can be used to measure and quantify the performance of the students in the exam. Thus, this is an example of quantitative data.
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g q4. how to understand causal system? if a lti system is non-causal, what does it mean in real life?
An output of a causal system is that whose inputs are just the past and the present. The outcome of a noncausal system depends on the upcoming inputs.
Define the term causal system?We will examine the connection between output as well as inputs to determine whether the provided system is causal or not.
You notice that the output Y (t) in the initial example depends on the input at hand because it equals X (t). As a result, the system is creating a relationship when the output is solely dependent on the current input, which is why it is causal in nature. Causal systems are those in which the system's output should not depend on or be independent of future values of the input, and in this case, the system's output is independent of future values since it is only dependent on the current values.Thus, there isn't a single example of an ontologically non-causal system, or one of a truly fundamental nature about which we can be sure, that we are aware of.
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academic advising: in 2014 the community college survey of student engagement reported that 32% of the students surveyed rarely or never use academic advising services. suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. in a simulation we select random samples from this population. for each sample we calculate the proportion who rarely or never use academic advising services. what is the smallest sample in the list below that will satisfy the conditions for the use of a normal model to represent the sampling distribution?
The smallest sample in the following list that meets the requirements for using a normal model to depict the sampling distribution is 0.0349.
What is standard deviation?A standard deviation (or) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. Statisticians have concluded that numbers with a margin of error of no more than 2 SD reflect measures that are closer to the real value than those with a margin of error more than 2SD. As a result, most QC procedures mandate that remedial action be taken for data points that consistently fall outside of the 2SD range.
Here,
Probability that students surveyed rarely or never use academic advising services = 32% = 0.32
In reality, students rarely or never use academic advising services at their college = 42% = 0.42
Sample size, n = 200
The sampling distribution of sample proportion will be approximately normal with mean.
therefore,
Mean, = p
= 0.42
now, the standard deviation is given using the formula
on substituting the respective values, we get
= √0.001218
= 0.0349
The smallest sample in the list below that will satisfy the conditions for the use of a normal model to represent the sampling distribution is 0.0349.
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2) Choose the equation of a line parallel to the given equation and passing through a point P.
-3x - y = - 4; P = (1, 4)
Equation of the line is y = -3x + 7.
What are parallel line ?Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines.
Suppose the line's equation is y=mx + c, where m and c are unknowns.
Since it is parallel to the equation y = -3x + 4 and -3x - y = -4, its slope is now -3. So m = -3.
Additionally, point (1,4). Therefore, this should be satisfied by our line's equation.
Consequently, 4 = -3(1) + c
therefore c = 7
The line's equation changes to y = -3x + 7.
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a 50ft ladder is placed against a large building. the base of the ladder is resting on an oil spill, and it slips at the rate of 3 ft. per minute. find the rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building.
The rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building is -3 ft./min.
The rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building is -3 ft./min. This rate takes into account the fact that the ladder is slipping at a rate of 3 ft./min. As the base of the ladder is slipping away from the building, the top of the ladder is moving down, hence the negative rate of change. This rate of change will remain the same until the base of the ladder has slipped the full 50 ft. from the base of the building. At this point, the rate of the change of the height of the top of the ladder will be 0, since the ladder will no longer be slipping.
The rate of change can be calculated as follows:
Rate of change = Change in height / Change in time
Change in height = Initial height - Final height
Initial height = 50 ft.
Final height = 50 ft. - 30 ft. = 20 ft.
Change in time = 30 ft. / 3 ft./min. = 10 min.
Rate of change = (50 ft. - 20 ft.) / 10 min. = -3 ft./min.
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Help please! I will mark brainliest.
Problem Walkthrough: Find the area of this figure.
Use 3.14 to approximate pi.
F
6
9
To solve for the area, split the figure into simple figures as
shown below. Solve for the area of each and combine.
6
Triangle
6
9
Rectangle
Half-circle
Enter the value
that belongs in
the green box.
Total Area
12
Answer:
86.13
Step-by-step explanation:
area of Triangle: ½ × height × base = ½ ×6×6= 18 cm
area of Rectangle: length × width= 6×9 = 54 cm
area of circle= π × (radius)² then...
area of Half-circle = [π×(radius)²] ÷2 = [3.14×(6/2)²] ÷2 = 14.13 cm
The Area of this figure= 18 + 54 + 14.13 = 86.13 cm
Answer:
[tex]A = 86.13[/tex]
Step-by-step explanation:
In order to find the area of the given figure
We need to divide the figure Into the following shapes
Firstly,
A triangle
Rectangle
Semi Circle
Area of a triangle + Area of a rectangle + Area of a semi circle = Area of the whole figure
So lets find the area of the figures
Area of Triangle = [tex]\frac{1}{2}[/tex]X[tex]6[/tex]X[tex]6[/tex]
= [tex]18[/tex]
Area of a rectangle = [tex]l[/tex]x[tex]b[/tex]
= [tex]9[/tex]x[tex]6[/tex]=[tex]54[/tex]
Area of a semi circle = [tex]\frac{1}{2}\pi r^{2}[/tex]
= [tex]\frac{1}{2} X \frac{22}{7} X(3)^{2}[/tex]
= [tex]14.13[/tex]
[tex]A = 18 + 54 + 14.13[/tex]
[tex]A = 86.13[/tex]
The total area of the geometry will be 86.13 square units.
Pls Mark me Brainliest
What is the equation of the line that passes through the point (-3,4) and has a slope of 2/3?
A line with a slope of 2 and a point at (4,3) satisfies the equation y = 2x - 5.
Which equation's formula is it?Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.
What do a line's two equations look like?In general, a straight line has the equation y = mx + c, where m denotes the gradient and y = c denotes the point at which the line intersects the y-axis. do s s., s. s s.. s... s.. A straight line with a gradient of m and an intercept of c on the y-axis has the equation y = mx + c.
Here,
given: slope of 2/3
the line that passes through the point (-3,4)
using formula
=> y = mx + c.
=> (y-y') = m(x-x') + c
=> (y-4) = 2/3(x+3) + c
=> y = 2x - 5.
Thus equation comes out to be y = 2x - 5..
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PLS HELP WITH THIS ASSIGNMENT OMG ITS SO HARD FOR ME
The new coordinates of each of the triangle coordinates are;
1) A'(-12, 6), B'(3, 9), C'(-9, 18)
2) A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)
3) X'(-8, 2), Y'(2, 14), Z'(8, 8)
4) X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)
5) A'(-8, 4), B'(2, 6), C'(-6, 12)
6) X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)
7) X'(-20, 5), Y'(5, 35), Z'(20, 20)
8) A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)
How to carry out dilation in transformation?Dilation is defined as a type of transformation where an image size either increases or decreases but then has the same shape as the original one. Thus, we will just multiply each coordinate by the scale factor;
We are given the coordinates of both triangles as;
Triangle ABC = A(-4, 2), B(1, 3), C(-3, 6)
Triangle XYZ = X(-4, 1), Y(1, 7), Z(4, 4)
1) Dilate triangle ABC by a scale factor of 3 means we multiply each ABC coordinate by 3 to get;
A'(-12, 6), B'(3, 9), C'(-9, 18)
2) Dilate triangle ABC by a scale factor of 1/2 means we multiply each ABC coordinate by 1/2 to get;
A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)
3) Dilate triangle XYZ by a scale factor of 2 means we multiply each XYZ coordinate by 2 to get;
X'(-8, 2), Y'(2, 14), Z'(8, 8)
4) Dilate triangle XYZ by a scale factor of 1/4 means we multiply each XYZ coordinate by 1/4 to get;
X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)
5) Dilate triangle ABC by a scale factor of 2 means we multiply each ABC coordinate by 2 to get;
A'(-8, 4), B'(2, 6), C'(-6, 12)
6) Dilate triangle XYZ by a scale factor of 1/3 means we multiply each XYZ coordinate by 1/3 to get;
X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)
7) Dilate triangle XYZ by a scale factor of 5 means we multiply each XYZ coordinate by 5 to get;
X'(-20, 5), Y'(5, 35), Z'(20, 20)
8) Dilate triangle ABC by a scale factor of 1/4 means we multiply each ABC coordinate by 1/4 to get;
A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)
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Four and a half times a number increased by 4 equal to three and half times the number increased by 6.What is number?
The unknown number from the given phrase is 2.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, four and a half times a number increased by 4 equal to three and half times the number increased by 6.
Let the unknown number be x.
Now,
Four and a half times a number increased by 4
[tex]4\frac{1}{2}x+4[/tex]
Three and half times the number increased by 6
[tex]3\frac{1}{2}x+6[/tex]
Here, [tex]4\frac{1}{2}x+4[/tex]=[tex]3\frac{1}{2}x+6[/tex]
9/2x+4=7/2x+6
9/2x-7/2x=6-4
2/2x=2
x=2
Therefore, the unknown number is 2.
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Select an expression equivalent to 16¼ × 16⅔
[tex]Answer:\ \sqrt[12]{16^{11}}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\16^\frac{1}{4} *16^\frac{2}{3}=\\\\16^{\frac{1}{4} +\frac{2}{3} }=\\\\16^\frac{1*3+2*4}{4*3} =\\\\16^\frac{3+8}{12}= \\\\16^\frac{11}{12}= \\\\\sqrt[12]{16^{11}}[/tex]
PLEASE HELP QUICK I WILL GIVE BRAINLIEST
Answer:
z > 1 1/3
Step-by-step explanation:
See picture
your client has a horse that is traveling to compete in an international event. one of the export requirements is a negative test for equine infectious anemia (eia). the results need to be reported on the international health certificate (ihc). where can you send the blood sample for testing to obtain official results?
You can send the blood sample size to a certified laboratory for testing. The laboratory will provide official results that can be reported on the IHC. State and federal animal health departments and veterinary diagnostic laboratories are usually certified to provide this service.
To obtain official results for a negative test for equine infectious anemia (EIA) for an international event, you can send the blood sample to a certified laboratory for testing. You should contact your state or federal animal health department or a veterinary diagnostic laboratory to find a certified laboratory in your area. The laboratory will test the blood sample and provide the official results to be reported on the international health certificate (IHC). It is important to make sure you use a certified laboratory for the testing in order to ensure the results are accurate and can be accepted for the international event.
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in the decimal number 1238.654 the place value of 5 is
what is the sequence of the following tasks in a perceptron? initialize weights of perceptron randomly go to the next batch of dataset if the prediction does not match the output, change the weights for a sample input, compute an output
The sequence of steps you provided is generally correct for training a perceptron, although there are some additional steps that might be included in the process depending on the specific implementation.
Here is a more complete list of steps that might be followed in training a perceptron:
Initialize the weights of the perceptron randomly.For each sample in the training dataset:Compute the output of the perceptron for the given input using the current weights.If the predicted output does not match the desired output, update the weights of the perceptron using an optimization algorithm, such as gradient descent.Repeat the process for the next batch of samples in the dataset.Continue this process until the perceptron has been trained to make accurate predictions for the given input.It's important to note that the specific details of how the perceptron is trained will depend on the specific implementation, such as the optimization algorithm used to update the weights, the size of the training dataset, and the number of epochs (iterations) of training.
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Izzy's Frozen Treats sells both frozen yogurt and frozen custard by the ounce. Last week, Marco noticed that a 3-ounce cup of frozen yogurt cost less than a 3-ounce cup of frozen custard. Marco has $5 to spend at Izzy's Frozen Treats today. Which can he buy more of, frozen yogurt or frozen custard?
The item Marco will buy more between frozen yogurt and frozen custard given his budget and cost of each item is frozen yogurt.
Which item can he buy more of?Amount Marco has to spend = $5Cost of a 3-ounce cup of frozen yogurt = less than cCost of 3-ounce cup of frozen custard = cHence, a 3-ounce cup of frozen yogurt cost less than a 3-ounce cup of frozen custard.
Therefore, Marco will buy more frozen yogurt than frozen custard because of the cheap price.
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Line k has a slope of 1/3. Line j is perpendicular to line k and passes through the point (1,4). Create an equation for line j.
The equation of line j is x + 3y -13 = 0 which is perpendicular to line k.
How does one point slope?
The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).One of the three forms we can use to express a straight line is the point slope form, also referred to as the point-gradient form.This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.Line k is perpendicular to line j
m(j) = - m(k)
m(j) = -(1/3)
One slope one point formula:
y - y₁ = m( x - x₁ )
y - 4 = -(1/3)(x - 1)
3y - 12 = -x + 1
x + 3y -13 = 0
Hence, The equation of line j is x + 3y -13 = 0 which is perpendicular to line k.
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i need the answer to 9x5x2=9x please
Answer:
x=10
Step-by-step explanation:
Your cousin plays point guard for her community basketball team. When she plays in a game, five out of seven baskets she scores for her team are lay-ups.
If your cousin scores fourteen baskets for her team at Saturday night's game, how many were lay-ups?
If, during the course of the season, your cousin scores one hundred forty baskets for her team, how many were lay-ups?
If, over the course of several games, your cousin makes twenty lay-ups, how many total baskets did she score for her team?
The total number of lay-ups in 14 baskets is 10
The total number of lay-ups in 140 baskets is 100The total number of baskets in 20 lay-ups is 28The total number of lay-upsIn fourteen baskets
From the question, we have the following parameters that can be used in our computation:
Lay-ups = 5 out of 7 baskets
This means that
Lay-ups = 5/7 baskets
When the number of baskets is 14, we have
Lay-ups = 5/7 * 14
Evaluate
Lay-ups = 10
In one hundred forty baskets
From the question, we have the following parameters that can be used in our computation:
Lay-ups = 5 out of 7 baskets
This means that
Lay-ups = 5/7 baskets
When the number of baskets is 140, we have
Lay-ups = 5/7 * 140
Evaluate
Lay-ups = 100
The total number of basketsHere, we have
Lay-ups = 20
Recall that
Lay-ups = 5/7 baskets
So, we have
Baskets = 7/5 lay-ups
This gives
Baskets = 7/5 * 20
Evaluate
Baskets = 28
Hence, the number of baskets is 28
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A building manager is buying gravel and mulch for landscaping. He can spend no more than $250 and must cover at least 200 square feet. Gravel costs $2 per square foot, and mulch costs $0.25 per square foot. If the building manager wants to purchase only one material, can he? Explain your answer.
Answer:
No, the building manager cannot purchase only one material. The maximum amount he can spend is $250, and 200 square feet of gravel would cost $400, which is more than the budget allows. Similarly, 200 square feet of mulch would cost only $50, which is far less than the budget allows.
Step-by-step explanation: