Therefore ,the volume of the block after cutting out the smaller cubes is (8/25 cm^2)
What is volume ?Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.
Volumes vary depending on the shape. We have examined different three-dimensional objects and shapes in geometry, including cubes, cuboids, cylinders, cones, and more. We will learn how to calculate the volume for each of these shapes.
Here,
volume = (8/25 cm2) represents the block's volume after the smaller cubes have been removed.
First, we must determine the volume of a cube with four or five centimeter sides, which is:
V = (4/5 cm)^2 = (16/25 cm^2)
The volume of each of the eight smaller cubes that was removed must now be subtracted.
v = (1/5 cm)^2 = (1/25 cm^2)
After the smaller cubes are removed, the block's volume is:
V - 8v = (16/25 cm^2) - 8*(1/25 cm^2) = (8/25 cm^2)
Therefore ,the volume of the block after cutting out the smaller cubes is (8/25 cm^2)
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nasa is conducting an experiment to find out the fraction of people who black out at g forces greater than 6. in an earlier study, the population proportion was estimated to be 0.43. how large a sample would be required in order to estimate the fraction of people who black out at 6 or more gs at the 99% confidence level with an error of at most 0.03? round your answer up to the next integer.
The sample size of 502 should be the required size to perform the experiment.
The confidence interval (1 - alpha )% for population percentage p is as follows,
CI =p +- z √pq/n
The following formula is used to determine the margin of error,
MOE = z * √pq/n
The information provided is, with a margin of error of 0.03 and = 0.32.
The z-value for an 85% degree of confidence is,
For the z-value, use a z-table.
The sample size n is then determined by,
MOE = z * √pq/n
= 1.44 √ 0.32( 1 - 0.32 ) ²/ 0.03
= ( 22.392 )²
= 502
Therefore, a sample of size 502 would be needed to assess the percentage of subjects that experience blackouts at 6 or more Gs.
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Let p: it is raining
Let q: robert is laughing.
Assume p is true. select two statements that must logically be true.
A. p ∨ q
B. p ∧ q
C. q → p
D. p → q
E. q ↔ p
The two statements that are logically true as per the given data is q=>p and p ∧ q .
p = raining
q = Robert is laughing
q=>p this is because the entire proposition is logically true when the conclusion of the condition is true.
and
p ∧ q means that it is raining and Robert is laughing which is again logically true.
If two logical statements have the same truth value in all circumstances, they are said to be comparable. This fact can occasionally be used to demonstrate a mathematical result by switching out one expression for an equivalent one while maintaining the original compound proposition's truth value.
Propositional types based on Truth values
tautologycontradictioncontingency.To learn more about proportional equivalence
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When given these two equations:
y = 2x + 4
y = 3x - 6,
How would I set up these systems of equations so that I could find the solution?
O Manipulate my variables to have the same coefficient, but different signs
O Make the two equations equal to each other and solve
O add the equations together
O subtract the equations together
There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer:
subtract the equations
Step-by-step explanation:
the second answer option is nonsense.
if the equations really have exactly one solution, then it is impossible to make them equal.
if 2 equations can be made equal, that means they have infinitely many solutions.
the other answers have all some merit.
but the last one (subtract the equations) is the best one.
it means
y = 2x + 4
- y = 3x - 6
------------------
0 = -x + 10
after adding x to both sides we get
x = 10
with that we use any of the 2 basic equations to get y :
y = 2x + 4 = 2×10 + 4 = 24
this worked right away, because the y terms have the same coefficients (1). so, by subtracting one equation from the other we eliminate y as variable and can solve for x.
if that was not the case like in
2y = 4x + 8
y = 3x - 6
we would have to do some transformation or manipulation to bring the system into a form like here in the beginning.
and the first and the third answer option would apply.
On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0. 62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0. 71. A random sample of 40 workers was selected from Company B and another random sample of 40 workers was selected from Company C. The proportion of workers from Company B who purchased coffee was
The correct unit of measure for the mean of the sampling distribution of (pˆB - pˆC) is Workers , the correct option is (d) .
In the question ,
it is given that ,
the proportion of workers who purchase coffee from company B is = 0.62
the proportion of workers who purchase coffee from company C is = 0.71
the random sample taken from company B is = 40 workers
the random sample taken from company C is = 40 workers
we know that , a proportion is written as two equivalent fractions.
So , Each ratio compares the same units, percentage of workers purchasing the coffee in the restaurant,
hence, the unit of measure for the mean of sampling distribution is workers .
Therefore , the unit for the measurement for the mean is (d) Workers .
The given question is incomplete , the complete question is
On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0.62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0.71. A random sample of40 workers was selected from Company B and another random sample of 40 workers was selected from Company C. The proportion of workers from Company B who purchased coffee was pˆB=0.70 and the proportion of workers from Company C who purchased coffee was pˆC=0.75.
What is the correct unit of measure for the mean of the sampling distribution of pˆB - pˆC ?
(a) Days
(b) Dollars
(c) Companies
(d) Workers .
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Tori bought one share of Chipotle stock on Nov 1, 2016 for $396.33.
Then, four years later, she sold it at the closing price of $778.38.
a) How much money did she gain/lose with this stock?
b) What was Tori's return on investment?
a) The amount of money that he earned with the stock was of: $382.05.
b) The return on the investment was of: 96.40%.
How to obtain the amount of money earned and the return on the investment?The amount of money earned is obtained by the subtraction of the price that the stock was sold by the price the stock was bought. If this amount is negative, it means that money was lost, otherwise money was earned.
Considering the values on the problem, the amount that he earned with the stock is given as follows:
778.38 - 396.33 = $382.05.
The return on the investment is given by the amount earned/lost divided by the initial value, and multiplied by 100% to obtain the value as a percentage, hence it is of:
382.05/396.33 x 100% = 96.40%.
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3x + 5y = 5
-2x-8y = 6
How can you eliminate the x-terms in this system?
3x + 5y = 5
Multiply by ? on both sides.
-2x8y=-6
Multiply by ?
on both sides.
Answer:
3x + 5y = 5
Multiply by 2 on both sides.
-2x - 8y = -6
Multiply by 3 on both sides.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} \;\;\:3x + 5y = 5\\-2x-8y = 6\end{cases}[/tex]
To eliminate the x-terms in the given system of equations:
Multiply 3x + 5y = 5 by 2 on both sides.Multiply -2x - 8y = 6 by 3 on both sides>3x + 5y = 5 → Multiply by 2 on both sides:
[tex]\implies 2(3x+5y)=2(5)[/tex]
[tex]\implies 6x+10y=10[/tex]
-2x - 8y = 6 → Multiply by 3 on both sides:
[tex]\implies 3(-2x - 8y) = 3(6)[/tex]
[tex]\implies -6x - 24y = 18[/tex]
Add them together to eliminate x:
[tex]\begin{array}{crcccc}&6x&+&10y&=&10\\+&(-6x&-&24y&=&18\\\cline{2-6} &&-&14y&=&28\end{array}[/tex]
7) what are the coordinates of the vertices with the base b and the height h?
8) solve for the measures of angles 1, 2, and 3
The coordinates of the vertices with the base b and the height h is O(0, 0), W(b, 0), T(b, h) and S(0,h).
What is rectangle?
An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.
The rectangle with base b and height h.
We know that:
The point O is shown in the graph is at Origin.
So, its coordinates are O(0, 0)
Since, the height of the rectangle is h,
as S and T are h units away from the x-axis.
and the base of the rectangle is b, T and W are b units away from the y-axis.
thus the coordinates of the other vertices are:
S(0, h), T(b, h) and W(b, 0)
Therefore, the coordinates of the vertices of the following rectangle with base b and height h are:
O(0, 0), W(b, 0), T(b, h) and S(0,h)
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in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
HELP ME
The number of bacteria after 4 hours is 800
How to determine the number of bacteria after 4 hours?The complete question is added at the end of this solution
Given that,
Initial population = 50Reproduction = splitting every hourThis means that the rate of production is by doubling
So, we have the following parameters
a = 50
r = 2
An exponential function is represented as
A(n) = arⁿ
Substitute the known values in the above equation, so, we have the following representation
A(n) = 50(2)ⁿ
We have to find,
Find the number of bacteria after 4 hours.
This means that n = 4
So, we have
A(4) = 50(2)⁴
Evaluate
A(4) = 800
Hence, the population is 800
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Complete question
in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
Find the number of bacteria after 4 hours.
A customer pays an initial fee and a daily fee to rent a snowmobile. The total payment for 3 days is 92 dollars. The total payment for 5 days is 120 dollars. What is the daily fee?.
A snowmobile can be rented for $14 per day with a $50 initial fix cost.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Let the initial fee be x and daily fee be y,
92=x+3y
120=x+5y
x+5y=120
x+3y=92
Subtract both,
2y=28
y=$14
x+5y=120
x+70=120
x=$50
The daily fee to rent a snowmobile is $14 per day with a initial fix fee of $50.
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A website displayed the following formula for the volume of a cone.
V = 1/3 nrh
James had never seen this formula before, but he knew there must be a typographical error in this formula. How could he tell
there was an error?
A. The calculated volume would be in linear units instead of cubic units.
B. The calculated volume would be in square units instead of cubic units.
C. The calculated volume would be in cubic units instead of square units.
D. The calculated volume would be in square units instead of linear units
James will declare the error by saying that the calculated volume would be in cubic units instead of square units.
What formula is correct for volume of cone?A cone has circular base and smooth curved surfaces that ends at the top.
volume of cone formula is denoted by V = 1/3×(πr²h) cubic unit
r is the radius of base of cone
h is the height of cone
π =3.142
hence, James needs to say that the unit of volume of cone should be written in cubic
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A teacher grades 27 tests in 3 hours.
find the constance of variation
Answer: 9
Step-by-step explanation:
27 divided by 3 is 9 so 9 is the constant variation
Bryan says that every equation that has one variable has a solution to it. Disprove Bryan’s assertion with two counterexamples.
Bryan's assertion is not true. Here are two counter examples to disprove it:
1) x = 0
This equation has only one variable, x, but it has no solution because there is no value of x that will make the equation true.
2) x^2 + 1 = 0
This equation also has only one variable, x, but it has no solution because there is no value of x that will make the equation true.
These examples show that it is possible for an equation with one variable to have no solution.
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(x2 – 2x – 37) ÷ (x2 – 3x – 40)
Answer:
If you divide:
[tex]1+\frac{x+3}{x^2-3x-40}[/tex]
If you simplify:
[tex]\frac{x^2-2x-37}{(x-8)(x+5)}[/tex]
Step-by-step explanation:
a triangle has two sides of length 18 and 3. what is the largest possible whole-number length for the third side?
Answer:
20
Step-by-step explanation:
Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.
And 18+3... 21, that is smaller than 21.
If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.
Please help, I don't quite understand.
Answer:
[tex]y=-\frac{3}{4}x-2[/tex]
Step-by-step explanation:
Substitute into point-slope form and rearrange to slope-intercept form.
[tex]y+8=-\frac{3}{4}(x-8) \\ \\ y+8=-\frac{3}{4}x+6 \\ \\ y=-\frac{3}{4}x-2[/tex]
On a coordinate plane, how are the location of the point (1 , -5) and (1 , 5) related?
Reflection across the y-axis on a coordinate plane.
What is the short definition of a coordinate plane?
Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is a single horizontal number line. The y-axis is a vertical number line, which is the other number line. A place known as the origin is where the two axes collide. The coordinate plane allows us to graph points, lines, and more.
What is reflaction of coordinate plane?
Transformation is the process of making each point in a shape appear at the same distance on the other side of a specified line.
The term "line of reflection" refers to introspection with relation to that line. A line is crossed to flip the image.
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Sophie was offered a job after college earning a salary of $30,000. She will get a raise of $2,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company
.
Answer:
Step-by-step explanation:
Sophie was offered a job after college earning a salary of $30,000. She will get a raise of $2,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.
HELP ASAP 100 POINTZZZZZZ
ollow the instructions below.
(a) Rewrite the percentage in the sentence below as a decimal. Decimal:
In a recent poll, 5% of the people surveyed were in favor of the new law.
(b) Rewrite the decimal in the sentence below as a percentage. Percent:%
The model was 0.274 of the size that the original was.
Decimal of 5% = 0.05, 0.274 to Percent:% 27.4%
What is percentage?A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The sign "%" is frequently put after the number to indicate percentages.
What is decimal?A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole amounts.
a).
so we have to write this in decimal that is remove percentage
To remove % we have , divide it by 100
suppose x% to remove % we divide it by 100, x% = x/100
5% = 5/100 =0.05 which is in decimal
b). The model was 0.274 of the size that the original was. we need to add percentage so to add percentage multiple it by 100
making x to percentage
x*100 = x%
so 0.274 to % will be
0.274 *100
27.4%
Decimal of 5% = 0.05, 0.274 to Percent:% 27.4%
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Determine the monthly periodic interest rate on a credit card with a 24.99% APR. Write your answer as a percent, rounded to the nearest hundredth.
The monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .
The average interest rate for new credit card offers is lower than the 24.99% APR on a credit card. If the cardholder keeps a balance on the credit card for the entire year, the APR of 24.99% means that the balance will rise by around 24.99%. If the APR is 24.99%, for instance, and you carry a $1,000 balance for a year, you would end up owing about $246.48 in interest.Fortunately, if you pay the entire balance before the due date each month, you won't be subject to the 24.99% APR. But you'll end up spending a significant amount in interest if you carry a balance from month to month.This is because interest costs accumulate every day the balance is outstanding. In other words, interest is applied to your principal balance as well as any accumulated interest from prior days.The credit card company will divide the APR using a daily periodic rate (DPR) to calculate the amount of interest you'll pay for a specific billing cycle because some months have more days than others. Simply divide a credit card's APR of 24.99% by 365 to obtain the DPR. The rate that results is 0.0685% each day. Until the payment is paid in full, daily interest charges are assessed.Hence, the monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .
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If 80% of 120 students passed the test, and (1)/(4) of these students received an A on the test, how many students received an A?
A 20 students
B 22 students
C 24 students
D 26 students
24 students received an A on the test.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
If 80% of 120 students passed the test, the number of students who passed is 120 * 80% = 96 students.
If (1)/(4) of these students received an A on the test, the number of students who received an A is (1)/(4) * 96 = 24 students.
Therefore, 24 students received an A on the test.
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An item is regularly priced at $83. It is on sale for 35% off the regular price.
Answer: $53.95
Step-by-step explanation:
Original Price: $83
Discount: 35%
35%=0.35
$83 x 35%, or 83 x 0.35
=29.05
$83-29.05
=$53.95
HELP!!!!!
I put a picture down below!
Answer:
d) y = -3x-3
e) y = -3x - 1
f) y = -3x + 2
Step-by-step explanation:
Knowledge Needed:
Slope-Intercept Form: y = mx + b
y and x stay as variables so you can solve for the intercepts and graph.
m is the slope, or the constant amount that the y-value on a line changes when the x-value increases by 1.
b is the y-intercept, or when t he line has an x-value of 0.
When lines are parallel, they have the same slope.
Question
d)
Examine the line: At what y-value does the line have a x-value of 0?
y-value: -3
Alternatively, you could also solve be getting a set of points on the line and plugging in.
(1,0)
Our equation for line d:
y = -3x - b
0 = -3(1) - b
0 = -3 - b
0 + 3 = -3 + 3 - b
3 = -b
b = -3
d) y = -3x-3
e)
Repeat the same steps.
y-intercept: -1
Because they are parallel, they have the same slope.
e) y = -3x - 1
f)
Repeat the same steps.
y-intercept: 2
Because they are parallel, they have the same slope.
f) y = -3x + 2
Which statement about the graph of y=12·(1/2)x is true?
The graph has an asymptote at y = 0.
Option (A) is correct.
What is the asymptote of the graph?
An asymptote is a straight line that constantly approaches a given curve but does not meet at an infinite distance. In other words, an Asymptote is a line that a curve approaches as it moves toward infinity.
The given function is:
[tex]y = 12.(\frac{1}{2})^x[/tex]
Now let's draw the graph for this given function,
By observing the graph we can conclude that the graph has an asymptote at y = 0 cause it is not meeting to the x-axis when it is approaching infinity.
Hence, the graph has an asymptote at y = 0.
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While working a summer job, Evelyn earned $198.10 in 7 hours. Find the rate of change.
Answer:
$221
Step-by-step explanation:
domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this
The reasonable domain is { 1,2,3,4,5 }
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.
Here, the situation is not given.
So, the reasonable domain is { 1,2,3,4,5 }
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What is the major difference between the alternate hypothesis and the null hypothesis?.
The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.
Hypothesis;-
A put forward explanation for a phenomenon is called a hypothesis (plural: hypotheses).
A hypothesis cannot be called a scientific hypothesis unless it can be tested using the scientific process. Observations from the past that cannot be fully explained by the body of knowledge at this time often serve as the foundation for scientific ideas.
A scientific hypothesis is distinct from a scientific theory, despite the fact that the phrases "hypothesis" and "theory" are sometimes used interchangeably.
A working hypothesis is a theory that has been accepted provisionally and is put forth for further investigation[1], beginning with an educated guess or way of thinking.
As a result, the alternative hypothesis of a test indicates the effect or relationship that your research predicts, whereas the null hypothesis of a test always predicts that there will be no effect or no association between variables.
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Which number represents a square root of 3 cos
3 [cos()+isin()]?
2
O √[cos()+sin()]
8
O
√3 cos (1) + i sin()]
5
O √3 [cos (STT)+isin (STT)]
6
O
3π
√3 [cos (3T) + sin(3)]
i
2
Square root of 3 cos
Consider the given data.
[tex]$$\begin{aligned}& \sin \theta+\sin ^2 \theta=1 \\& \sin \theta=1-\sin ^2 \theta \\& \sin \theta=\cos ^2 \theta\end{aligned}$$[/tex]
We have,
[tex]$$\begin{aligned}& =\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta+2 \cos ^4 \theta+2 \cos ^2 \theta-2 \\& =\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta+2\left(\cos ^4 \theta+\cos ^2 \theta-1\right) \\& =\left(\cos ^4 \theta+\cos ^2 \theta\right)^3+2\left(\cos ^4 \theta+\cos ^2 \theta-1\right)\end{aligned}[/tex]
[tex]$$Since, $\sin \theta=\cos ^2 \theta$Therefore,$$\begin{aligned}& =\left(\sin ^2 \theta+\sin \theta\right)^3+2\left(\sin ^2 \theta+\sin \theta-1\right) \\& =1^3+2(1-1) \\& =1+0\end{aligned}[/tex]
[tex]=1[/tex]
Hence, the required value is 1.
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(a) Find m ZK.
40°
6
m2K =°
K
6
Step-by-step explanation:
it is an isoceles triangle (both legs are equally long).
that means also both base angles are equal :
angle J = angle L = 40°
the sum of all angles in a triangle is always 180°.
so,
180 = angle J + angle L + angle K = 40 + 40 + angle K
angle K = 180 - 40 - 40 = 100°
the width of a confidence interval for a population mean depends on group of answer choices the sample proportion. the population size. the level of confidence chosen. the sample mean.
The width of a confidence interval for a population mean depends on group of answer choices the sample proportion is population size and sample mean .
Given :
What is population size ?
population is the entire set of items from which you draw data for a statistical study. It can be a group of individuals, a set of items, etc.
What is sample mean ?
The sample mean from a group of observations is an estimate of the population mean .
so the width of a confidence interval is dependent on population size and sample mean .
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Theo drove 240 miles in 4 hours. Lex drove 183 miles in 3 hours. At those rates, could either man drive 118 miles in 2 hours? Complete the explanation. Show your work pls
Answer:
Yes, both men could drive at the rate of 112 miles in 2 hours. This is because you need to find the unit rate. For Theo's unit rate it is 57 miles per hour while Lex could drive at 62 miles per hour. Finally, the last statement ask if they could drive at a unit rate of 56 miles per hour and yes both men can.
Step-by-step explanation:
Answer: Theo's speed is 240 miles / 4 hours = <<240/4=60>>60 mph.
Lex's speed is 183 miles / 3 hours = <<183/3=61>>61 mph.
To determine whether Theo can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 60 mph: 118 miles / 60 mph = <<118/60=1.97>>1.97 hours.
Since 1.97 hours is less than 2 hours, Theo could drive 118 miles in 2 hours.
To determine whether Lex can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 61 mph: 118 miles / 61 mph = <<118/61=1.93>>1.93 hours.
Since 1.93 hours is less than 2 hours, Lex could also drive 118 miles in 2 hours.
Therefore, both Theo and Lex could drive 118 miles in 2 hours.