Step-by-step explanation:
The two triangles are similar so the ratios of their legs are equal:
\(\dfrac{x}{3}= \dfrac{8}{4}\)
Solving for x, we get
\(x = 6\)
Can someone help me please?
Answer:
Step-by-step explanation:
the dot would either (1,4) or (4,1)
a squared+ b squared= c squared
the length of the sides are 3
3 squared + 3 squared= c squared
9+9 =c squared
18= c squared
square root of 18 rounded to the nearest tenth is 4.2
−1 ≤ x/-4 − 3
Solve the inequality. Show all steps.
Answer:
≤ − 8
Step-by-step explanation:
-1 ≤ \(\frac{x}{-4}\) -3
4 ×(-1) ≤ 4 × \(\frac{x}{-4}\) -4×3
-4 × (-1) ≤ -x - 4×3
-4 ≤ -x - 12
x ≤ -12 + 4
x ≤ -8
what is the value of b?
Answer:
24
Step-by-step explanation:
2b = b+24
2b-b = 24
b = 24
What is the measure of Z ABC ? B 60° 60° c
Answer:
60°
Step-by-step explanation:
If it a equilateral triangle
This morning, Kendall drank a cup of coffee that had 95 milligrams of caffeine in it. She didn't have any more caffeine for the rest of the day. Kendall read online that the amount of caffeine in her body will decrease by approximately 13% each hour. Write an exponential equation in the form y=a(b)x that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = ____. To the nearest milligram, how much caffeine will be in Kendall's body after 12 hours?
An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is
The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.
What is an exponential function?In Mathematics, an exponential function can be modeled by using the following mathematical equation:
f(x) = a(b)^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:
Rate of change (decay rate) = 100 - 13 = 87% = 0.87.
By substituting the parameters into the exponential equation, we have the following;
\(f(x) = 95(0.87)^x\)
When x = 12, we have;
\(f(12) = 95(0.87)^{12}\)
f(12) = 17.86 ≈ 18 milligrams.
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the question is in the picture attached
A line of best fit, also known as a regression line, is a straight line that best represents the relationship between two variables in a scatter plot. The association between the variables is strong.
How do you know strong association using line of best fit?To determine whether there is a strong association between the two variables, you need to examine the pattern of the data points in relation to the line of best fit.
If the data points are tightly clustered around the line of best fit, this indicates a strong association between the two variables. On the other hand, if the data points are more spread out and do not follow a clear pattern, this suggests a weak association.
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2 QUESTIONS!
When a number is decreased by 10% of itself, the result is 27. What is the number?
Write an equation to model the problem. Use a to represent the number.
Answer:
Solve the equation to find the number:
Answer:
Answer:
30
Step-by-step explanation:
The equation will be:
x - (10% of x) = 27
x - 0.1x = 30
0.9x = 30
Divide by 0.9
x = 30
The number is 30
Second question:
Length = 2x - 3
Width = x
Perimeter = 72
Perimeter = 2(l + w)
= 2(2x - 3 + x) = 72
4x - 6 + 2x = 72
6x = 72 + 6
6x = 78
w = 78/6 = 13
The width is 13 meters
I NEED HELP PLS I need the base and volume of this pic should be above pls help
Answer:
Area of the base=16m squared
Volume of the figure =21m cubed
What fraction of an hour is 51 minutes?
Give your answer in its simplest form.
Answer:
0.850
Step-by-step explanation:
what is the equation for the perpendicular bisector of the line segment whose endpoints are (-7, 2) and (-1,-6)
The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.
To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.
Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)
= (-8/2, -4/2)
= (-4, -2)
The midpoint of the line segment is (-4, -2).
Next, we need to find the slope of the line segment using the slope formula:
Slope = (y2 - y1)/(x2 - x1)
Slope = (-6 - 2)/(-1 - (-7))
= (-6 - 2)/(-1 + 7)
= (-8)/(6)
= -4/3
The slope of the line segment is -4/3.
Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.
Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:
y - y1 = m(x - x1)
y - (-2) = (3/4)(x - (-4))
y + 2 = (3/4)(x + 4)
y + 2 = (3/4)x + 3
y = (3/4)x + 1.
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Is this statement true or false?
Ore is a chunk of rock that contains a large amount of metal. Most minerals come from rock that is mined from the Earth’s crust^,^
Label if it is binomial or monomial or trinomial
3x+9
2xy+7
5x^2+2x-6
8xy+2y+5
-3y
13x+1
10xy^2
Answer:
Binomial
Binomial
Trinomial
Trinomial
Monomial
Binomial
Monomial
What are the positive and negative square roots of 3,600?
Answer:
60 and -60
Hope this helps! :)
Shantel told her hired hand Warren to gather eggs from the henhouse. Warren collected 30 eggs and brought them to Shantel. Shantel inspected
them and complained that 40% of them were broken. How many of them were still good eggs?
eggs were still good.
Answer:
18 eggs are still good.
Step-by-step explanation:
If 40% was broken then 60% are still good.
30(.6) = 18
Answer: 18 eggs were not broken and considered good.
Step-by-step explanation: 30 x 40% is the amount of eggs that were broken.
30 x 60% would be the amount of eggs that were still good.
This is becuase the total percentage must add up to be 100% between good eggs and broken eggs.
30 x .60 = 18 So 18 eggs were good
30 x .40 = 12, so that was the number of eggs that were broken
You could have done this problem two ways. Either calculate the broken eggs and subtract from the total. 30-12 = 18, or you could have just calculated the correct amount from figuring the percentage of eggs that were good from the beginning.
how do you solve 2/5g=3/5 with a whole number??? I'm stuck
Answer:
g = 3/2
Step-by-step explanation:
Step 1: Multiply both sides by 5 (the whole number).
\(\frac{2}{5}g * 5 = \frac{3}{5} * 5\) \(2g = \frac{15}{5}\) \(2g = 3\)Step 2: Divide both sides by 2.
\(2g/2 = 3/2\) \(g = 3/2\)Therefore, g = 3/2.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
g = 1\(\frac{1}{2}\)
Step-by-step explanation:
\(\frac{2}{5} g = \frac{3}{5}\)
Multiply both sides by \(\frac{5}{2}\) the reciprocal of \(\frac{2}{5}\).
\(g = \frac{3}{5}\) ×\((\frac{5}{2})\)
Multiply \(\frac{3}{5}\) times \(\frac{5}{2}\) by multiplying numerator times numerator and denominator times denominator.
\(g = \frac{3x5}{5x2}\)
Cancel out 5 in both numerator and denominator.
\(g = \frac{3}{2}\)
simplify
1\(\frac{1}{2}\)
Hope it helps and have a great day! =D
~sunshine~
Calc question — related rates
The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
How to determine rate?The volume of the liquid in the bowl is given by the following integral:
\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)
where r = radius of the bowl and y = height of the liquid.
The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:
r = √{(4/(8-x)) - 1}² + 1²
The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:
h = (4/(8-x)) - 1
Substituting these equations into the volume integral:
\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)
Evaluate this integral using the following steps:
Expand the parentheses in the integrand.
Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.
Integrate each part separately.
The integral of the square root term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)
The integral of the linear term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)
Substituting these formulas into the integral:
V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h
Evaluating this integral:
V = π { 16/27 (8-h)³ - 16/18 (8-h)² }
The rate of change of the volume of the liquid is given by:
dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }
The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.
Substituting these values into the equation for dV/dt:
dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π
Solving this equation for the rate of change of the depth of the liquid:
dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹
Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
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How many solutions does the equation -2a + 2a + 7 = 8 have
Step-by-step explanation:
-2a + 2a + 7 = 8
Solving like terms
7 = 8
= 8 - 7 = 1
Has one solution
7.) According to the quantity equation, changes in the money supply will lead directly to
changes in the price level if velocity and real GDP are unaffected by the change in the
money supply. Will velocity change over time? What factors might lead to changes in
velocity? Are those changes related to changes in the money supply?
According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.
For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.
For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.
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3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
What is the multiplicative rate of change for the exponential function f(x). =(5/2)-x
The multiplicative rate of change for the function is approximately.
To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.
The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.
Using the chain rule, the derivative of is:
Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is
The value of ln(2/5) is approximately -0.916.
It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.
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the graph models the linear relationship between the number of mouthy payments made on a loan and the remaining balance in dollars left to pay on the loan. which statement describes the x-intercept of the graph?A) the x-intercept is 60, which represents the initial balance in dollars of the loan.B) the x-intercept is 27,000, which represents the initial balance in dollars of the loan C) the x-intercept is 60, which represents the number of monthly payments needed to replay the loan. D) the x-intercept is 27,000 which represents the number of monthly payments needed to replay the loan.
we have
x -----> number of monthly payments
y -----> remaining balance
Remember that
the x-intercept is the value of x when the value of y is zero
In this context
is the number of monthly payments when the remaining balance is zero
looking at the graph
the x-intercept is (60,0)
therefore
the answer is the option CPlease help thank you!!!
If the simple interest on $2,000 for 2 years is $280, then what is the interest rate?
Answer:
0,28percent
Step-by-step explanation:
If simple interest formula is = P X r X t
Then interest rate = p X t/ I
Activity
You have also set up a card game in which a player picks a card from a standard deck of 52 cards. The player wins if these two events occur together: E1, in which the card drawn is a black card, and E2, in which the card drawn is a numbered card, 2 through 10.
Question 1
What is the probability of getting a black card and a numbered card? Calculate the probabilities P(E1) and P(E2) as fractions.
The probability of getting a black card and a numbered card is 9/26.
To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.
There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).
Therefore, the probability of drawing a black card (P(E1)) is:
P(E1) = Number of favorable outcomes / Total number of possible outcomes
P(E1) = 26 / 52
Simplifying this fraction, we get:
P(E1) = 1/2
So the probability of drawing a black card is 1/2.
To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.
Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.
Therefore, the probability of drawing a numbered card (P(E2)) is:
P(E2) = Number of favorable outcomes / Total number of possible outcomes
P(E2) = 36 / 52
Simplifying this fraction, we get:
P(E2) = 9/13
So the probability of drawing a numbered card is 9/13.
To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:
P(E1 ∩ E2) = P(E1) × P(E2)
P(E1 ∩ E2) = (1/2) × (9/13)
Simplifying this fraction, we get:
P(E1 ∩ E2) = 9/26
Therefore, the probability of getting a black card and a numbered card is 9/26.
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when creating a variable for use in r, your variable name should begin with . 1 point an operator a letter a number an underscore 2. question 2 you want to create a vector with the values 21, 12
The multiplies each vector element by 2.
When naming a variable in R, it's best to start with a letter or an underscore. This is because R uses letters and underscores in variable names while using operators (e.g., +, -, *, /) for operations.
In R, use the c() function to create a vector. A vector is a data structure that stores a list of values in a specific order. To make a vector with the values 21 and 12, for example, write:
c - my vector (21, 12)
This produces a vector named "my vector" that contains two elements, 21 and 12. The elements of a vector can be accessed using square bracket notation:
my vector[1] # yields 21
my vector[2] # yields 12
You can also perform mathematical operations on vectors, and R will perform the operation element by element. As an example:
my vector * 2 # yields 42 24
This multiplies each vector element by 2.
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30% tip on a bill of $150.47
Answer:
45.141 or if you round 45.14
Step-by-step explanation:
150.47 x 0.30 = 45.141
What 68784 rounded to the nearest thousandth?
Answer: 6,9000
Step-by-step explanation:
Carleigh, Inc., is a pork processor. Its plants, located in the Midwest, produce several products from a common process: sirloin roasts, chops, spare ribs, and the residual. The roasts, chops, and spare ribs are packaged, branded, and sold to supermarkets. The residual consists of organ meats and leftover pieces that are sold to sausage and hot dog processors. The joint costs for a typical week are as follows: Direct materials $84,500 Direct labor 29,000 Overhead 20,000 The revenues from each product are as follows: sirloin roasts, $68,000; chops, $71,000; spare ribs, $33,000; and residual, $9,800. Carleigh’s management has learned that certain organ meats are a prized delicacy in Asia. They are considering separating those from the residual and selling them abroad for $52,000. This would bring the value of the residual down to $2,650. In addition, the organ meats would need to be packaged and then air freighted to Asia. Further processing cost per week is estimated to be $27,500 (the cost of renting additional packaging equipment, purchasing materials, and hiring additional direct labor). Transportation cost would be $12,100 per week. Finally, resource spending would need to be expanded for other activities as well (purchasing, receiving, and internal shipping). The increase in resource spending for these activities is estimated to be $3,120 per week.
Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.
To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.
The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).
Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.
However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).
Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.
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A concrete plant uses the following proportions per m3 of concrete: cement 310 kg; water 180 kg; fine aggregate 750 kg and coarse aggregate 1080 kg both in SSD conditions. If the fine aggregate in the field has 4% excess water find the revised quantity of water. cehgg
Answer:
150 kg
Step-by-step explanation:
Given that
cement = 310 kg
Fine aggregate = 750 kg
coarse aggregate = 1080 kg
mass of water = 180 kg
given that aggregate in field is 4% excess water
Determine the revised quantity of water
mass of concrete per m^3 = mass of cement + mass of water + mass of fine aggregate + mass of coarse aggregate
therefore mass of concrete = 310 + 180 + 750 + 1080 = 2320 kg
given that fine aggregate in field has 4% excess water this simply means it was void of air in the concrete the new weight = (1.04 * 750) = 780
Hence the revised quantity of water ( x )
= 310 + x + 780 + 1080 = 2320
therefore x = 150 kg
What graph would best display the data shown in the frequency table?
A. line plot
B. vertex-edge graph
C. histogram
D. stem-and-leaf graph
Answer:
histogram
Step-by-step explanation: