There are two ways
Explanation:
36x2=72
12x7=72
An animal shelter has 8 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the animal shelter?
well, the total amount is really "x", which oddly enough is the 100%, but we also know that 32% of that is 8, hmmmm
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 8& 32 \end{array} \implies \cfrac{x}{8}~~=~~\cfrac{100}{32} \\\\\\ \cfrac{ x }{ 8 } ~~=~~ \cfrac{ 25 }{ 8 }\implies 8x=200\implies x=\cfrac{200}{8}\implies x=25\)
\((f) = ex + 6\)
use the chain rule and the oppropriate rule to differniate each following function
The differentiation of the given function f(x) = eˣ+6 is eˣ
What is differentiation?The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given is function f(x) = eˣ+6, we need to find the derivative of this function,
f(x) = eˣ+6
f'(x) = d / dx (eˣ+6)
= d(eˣ)/dx + d(6)/dx
Since, 6 is a constant and derivative of a constant is zero,
d(eˣ)/dx + d(6)/dx = d(eˣ)/dx + 0
Now, when we differentiate eˣ, we get eˣ itself,
Therefore,
d(eˣ)/dx = eˣ
Therefore, the differentiation of the given function f(x) = eˣ+6 is eˣ
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The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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i need to know the slopes of these problems, they all the numbers are 1,2,3,4,5
Answer:
5 is 1
6 is 2/3
7 is 2/3
8 is 2
A diphosphonate kit contian 180 mCi of Tc99m in 30 ml when it is prepared at 8am. Immediately, a 20 mCi dose is withdrawn for a bone scan. if the patient arrives late at 9:30 and half the volume is accidentally discharged, how much volume from the kit must now be added to the syringe to correct the dose to 20 mCi? (no other doses have been withdrawn meanwhile, and the decay factor for 1.5 hrs is 0.841)
The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = Initial activity * Decay factor
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = Initial activity - 20 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = Remaining activity * Decay factor
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30
Calculate the remaining volume at 9:30:
Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume
Let's perform the calculations step by step:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = 180 mCi * 0.841 = 151.38 mCi
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = 180 mCi - 20 mCi = 160 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30
Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml
Calculate the remaining volume at 9:30:
Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml
Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
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8(7n-2) -6(7n+1)
Explain please
Answer:
8(7n - 2) - 6(7n + 1) = 14n - 22Step-by-step explanation:
8(7n - 2) - 6(7n + 1)
use the distributive property: a(b + c) = ab + ac
= 8 · 7n + 8 · (-2) + (-6) · 7n + (-6) · 1
= 56n - 16 - 42n - 6
combine like terms
= (56n - 42n) + (-16 - 6)
= 14n - 22
Answer:
=> 14n - 22
Step-by-step explanation:
8(7n-2) -6(7n+1)
=> 56n - 16 - 42n -6
=> 14n - 22
an edge can represent
Answer:
Edges are the components that are used to represent the relationships between various nodes in a graph. An edge between two nodes expresses a one-way or two-way relationship between the nodes. (hackerearth.com)
Step-by-step explanation:
PLS ITS LATE WORK NO DUMB ANSWERS
Answer:
day 2
Step-by-step explanation:
day 1 had a 26.19-degree change while day 2 had a 33.47
Answer:
Day 2 is a bigger change.
Step-by-step explanation:
Day 1 change: 26.19
Day 2 change: 33.47
Add the positive version of each number together to find the change, like so:
Day 1: -12.75 to 12.75 and 13.44 to 13.44 12.75+13.44= 26.19
Day 2: -8.83 to 8.83 and 24.64 to 24.64 8.83 + 24.64=33.47
PS: Next time, please be a little nicer with your question.
Please see screenshot.
Answer:
See below
Step-by-step explanation:
Create a dot plot of the data shown below.
20, 21, 21, 25, 20, 23, 27, 23, 24, 25, 26, 24, 23, 22, 24
Which measure of center would best describe a typical
value of the data set? Why?
would be best,
The mean
because the data distribution is
V nearly symmetrical
Intro
Click or tap the number line to add a dot.
20 21
22
23 24 25 26 27 28 29
Reset
Based on the data, the mean would be the best measure of center to describe a typical value in the data set.
How to create a dot plot with the given data?To create a dot plot, we can list the numbers in order and place a dot above the corresponding value on the number line.
20 ••
21 ••
22 •
23 ••••
24 •••••
25 ••
26 ••
27 •
The dot plot shows a relatively symmetric distribution of the data, with the majority of values clustered around the middle. Therefore, the mean would be a good measure of center to describe a typical value of the data set.
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Given the function R(x)=x+3x−4, find the values of x that make the function less than or equal to zero. Write the solution in interval notation.
The values of x that make the function less than or equal to zero are x ≤ -3 or x ≥ 4. This can be written in interval notation as (-∞, -3] ∪ [4, ∞).
The given function is R(x) = (x + 3)/(x - 4)
We have to find the values of x that make the function less than or equal to zero
We need to set the expression equal to zero and solve for x.
Let the function (x + 3)/(x - 4) = 0.
We can solve this equation by rearranging it to get x + 3 = 0, or x = -3.
We also get x - 4 = 0, or x = 4.
Therefore, the values of x that make the function less than or equal to zero are x ≤ -3 or x ≥ 4. This can be written in interval notation as (-∞, -3] ∪ [4, ∞).
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HEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLLLllllppppppppppppppp
Which of the equations below can be used to find the measure of ∠A?
A. tanA=9.46.7
B. A2=6.72+9.42
C. sinA9.4=sin906.7
D. cosA=6.79.4
The equation that can be used to determine the measure of ∠A is tanA = 9.4/6.7. The correct option is A. tanA=9.4/6.7
Trigonometry
From the question, we are to determine which of the given equations can be used to determine the measure of ∠A
In the diagram,
If ∠A is the included angle
Then,
Using SOH CAH TOA
Opposite = 9.4
Adjacent = 6.7
Thus,
tanA = 9.4/6.7
Hence, the equation that can be used to determine the measure of ∠A is tanA = 9.4/6.7. The correct option is A. tanA=9.4/6.7
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each equation of the piecewise function represented in the graph to its corresponding piece of the domain.
Answer:
one is 3-x
two is 1
three is x
four is 5-x
hope it helps :)
Answer:
1: 3-x
2: 1
3: x
4: 5-x
Step-by-step explanation:
Hope this helped
Write the following using algebraic notation, using the letter x for any
unknown numbers:
think of a number, double it, then add fifteen.
\( = x \times 2 + 15 \\ = 2x + 15\)
DOUBLING IT MEANS MULTIPLYING IT BY 2
THEN ADD 15 AS SHOWN ABOVE.
HOPE THIS HELPS
Simplify each expression by combining like terms:
9m-7m+13
Please explain if you can
help me please thank you
Answer:
m<A = 98.25
m<B = 81.75
m<C = 113
m<D = 113
m<E = 67
Step-by-step explanation:
3x + 12 + 5x - 18 = 180
8x - 6 = 180
8x = 186
x = 23.25
3x + 12
3(23.25) + 12
81.75
5x - 18
5(23.25) - 18
98.25
6y - 5 + 10y - 7 = 180
16y - 12 = 180
16y = 192
y = 12
6y - 5
6(12) - 5
67
10y - 7
10(12) - 7
113
A recipe for pancakes requires 3/4 cup of oil. If Mr. Darcy wants to triple the recipe, how much oil will he need?
What fraction is equivalent to the expression
21
16
÷
7
4
?
Answer:
3/4
Step-by-step explanation:
21/16 ÷ 7/4
21/16 × 4/7
3/4
HELP! WILL GIVE BRAINLIEST IF YOU'RE CORRECT!
a because it is correct,
-10/3 is same as - 10/3
A t-shirt requires 1 3/8 yards of material. How many t-shirts can be made from 41 1/4 yards of material?
Applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
How to Divide Fractions?In the problem given, we have the following information:
Material needed for one t-shirt = 1 3/8 yards
We want to find how many 1 3/4 we would find in 41 1/4.
Applying the knowledge of fraction, we are to divide 41 1/4 by 1 3/8. Convert both mixed fractions to improper fractions then divide:
41 1/4 ÷ 1 3/8
165/4 ÷ 11/8
165/4 × 8/11
165/4 × 8/11
15/1 × 2/1
= (15 × 2)/(1 × 1)
= 30/1
= 30.
Therefore, applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
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Plsssss helppppp
Would a piecewise function be a better model for capturing the data shown in all three
images? If so, what might the rules of that function be?
A piecewise function is a function defined by multiple sub-functions, each of which apply to a specific interval or subdomain of the total domain. The output of the piecewise function is determined by evaluating the appropriate sub-function for each input value based on the subdomain it belongs to.
What is a piecewise function?Piecewise functions are often used to model real-world situations where the behavior of the function changes under different conditions.
When an input value passes specific "boundaries," a rule or relationship changes. In these cases, we employ piecewise functions to explain the situation. For instance, it happens frequently in business that the price per piece of a particular item gets decreased after the quantity bought exceeds a certain threshold.
An overview was given as your information is incomplete.
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Each big square below represents one whole.
What percent is represented by the shaded area?
%
Answer:
91%
Step-by-step explanation:
Answer:
91%
Step-by-step explanation:
Count the white blocks: 9
and subtract them from the blue blocks: 100 - 9 = 91%
A man is disabled in an accident and wants to receive an insurance payment that will provide him with $2400 at the
end of each month for 20 years. If the payment can be placed in an account that pays 6% compounded monthly, what
size payment should he seek?
He should seek a payment of $
(Simplify your answer. Round to the nearest cent as needed.)
The man should seek a payment of $725.08
How to determine the size paymentThe amount of money he wants to receive can be calculated using the formula for compound interest:
A = P * (1 + r/n)^(nt)
where A = $2400 ---- final amount
P = principal
r = 6%, -- interest rate
n = 12 --- number of times the interest is compounded
t = 20, number of years (20).
So, we have
2400 = P * (1 + 6%/12)^(12 * 20)
This gives
P = 2400/3.310
Evaluate
P = 725.08
So, the man should seek a payment of $725.08
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Refer to the given terms . A pattern defines the relationship between the first two terms . Determine the relationship and identify the missing term of the second pair , such that both the pairs are analogous . AZP : ZAR :: TXK :
The missing term in the second pair is YUL.
To determine the relationship between the first two terms, let's analyze the given pattern: AZP : ZAR.
If we look closely, we can observe that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
So, applying the same pattern to the second pair (TXK), we need to shift each letter one position forward in the alphabet:
T + 1 = U
X + 1 = Y
K + 1 = L
Therefore, the missing term in the second pair is YUL.
The analogy between the pairs is that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
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graph the parabola x=1/2(y-2)^2-4. find and graph the vertex, focus, directrix, and focal chord endpoints.
1. Find the graph of the parabola attached below
2. Vertex (-4, 2) Focus (-7/2, 2) Directrix (x = -9/2) Endpoints (-7/2, 1) (-7/2, 3)
How do we find the vertex, focus, directrix, and focal chord endpoints or the parabola?For the parabola, x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,
Vertex → (h, k)
In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴ vertex (-4, 2).
focus → (h, k) = (-4, 2); P = 1/2
Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.
∴ Focus is (-4 + p, 2)
(-4 + 1/2, 2) ⇒ (-7/2, 2)
directrix → x = d
Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.
∴ x = -4 - p ⇒ x = -4 - 1/2
x = 9/2
focal chord endpoints →
The focus of the parabola is (-7/2, 2).
The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.
Therefore, the endpoints of the focal chord are:
(-7/2, 3) and (-7/2, 1).
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List and explain some expenditures and revenues in your personal budget
Some expenditures and revenues in personal budget are listed below.
What are expenditures and revenues in your personal budget?
Expenditures:
1. Housing: This includes rent or mortgage payments, property taxes, and utility bills.
2.Transportation: This includes the cost of owning and maintaining a vehicle, as well as any public transportation costs.
3. Food: This includes the cost of groceries and dining out.
4. Insurance: This includes health, car, and homeowner's or renter's insurance.
5. Personal Care: This includes expenses such as clothing, grooming, and personal hygiene products.
6. Entertainment: This includes expenses for hobbies, recreation, and leisure activities.
Revenues:
1. Salary: The money earned from a job or employment.
2. Investment Income: This includes money earned from stocks, bonds, and other investments.
3. Business Income: This includes money earned from a small business or self-employment.
4. Rent Income: This includes money earned from renting out property or other assets.
5. Government Benefits: This includes money received from programs such as Social Security and unemployment benefits.
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I need help doing this question
Answer:
the table is a representation of the graph
I can answer 1-3 though
1) the slope is 3 and represents hours to cost ratio
2) the y-intercept is 20 and represents the initial cost at 0 hours or the base amount Andy's repair costs (a job less than an hour)
3) 7 hours of labor and $440 is the cost
f(x) = 6x - 4g(x) = 3x² – 2x – 10Write (gof)(x) as an expression in terms of x.(gof)(x) =
Given
\(\begin{gathered} f(x)=\text{ 6x-4} \\ g(x)=3x^2-2x-10 \end{gathered}\)Solution
\(\begin{gathered} \text{gof(x)}=g(6x-4) \\ \text{gof(x)}=3(6x-4)^2-2(6x-4)-10 \\ \end{gathered}\)Expand the bracket
\(\begin{gathered} \text{gof(x)}=3(6x-4)(6x-4)^{}-2(6x-4)-10 \\ \text{gof(x)}=3(36x^2-48x_{}+16)^{}-2(6x-4)-10 \\ \text{open the bracket} \\ \\ \text{gof(x)}=108x^2-144x_{}+48^{}-12x+8-10 \\ \text{gof(x)}=108x^2-144x_{}+48^{}-12x-2 \\ \text{gof(x)}=108x^2-144x_{}-12x+48-2 \\ \\ \text{gof(x)}=108x^2-144x_{}-12x+46 \\ \text{gof(x)}=108x^2-156x+46 \end{gathered}\)The final answer
\(\text{gof(x)}=108x^2-156x+46\)The area of the rectangle is 25xy^2, what is the width and length
Answer:
25xy=L
y=W
Step-by-step explanation:
The width and length are
25xy=L
y=W
We factor this out and then we get 2 terms which are our factors
which of these consumers might depend on a rabbit for its energy?
a.horse
b.coyote
c.grasshopper
d.cow
Answer:
coyote
Step-by-step explanation: