Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $3 and the cost of mailing a package is $7. Can she mail 60 cards and 26 packages?
Answers
Answer:
Yes
Step-by-step explanation:
Simply plug in these values into our constraints and see if they work.
60 - 26(2) = 8
This meets the first constraint since 60 cards is 8 more than 2 times 26 packages.
Reiko can only spend $500 or less, so we have:
3(60) + 7(26) ≤ 500
180 + 182 ≤ 500
362 ≤ 500
This statement is in fact, correct.
Therefore, Reiko is able to mail 60 cards and 26 packages.
Related Questions
for what value of x is the square of the binomial x+1 one hundred and twenty greater than the square of the binomial x-3
Answers
Answer:
x=16
Step-by-step explanation:
(x+1)^2=(x-3)^2+120
x² + 2x + 1 = x² - 6x + 9 + 120
8x=128
x=16
30 POINTS!!! PLEASE HELP ME! ASAP
Answers
Answer:
I think is higher
Step-by-step explanation:
Craig has acollection of 220 marbles. He lets his friend have 1/4 of his collection and sells 1/5 of his collection to the novelty store. He takes 15 marbles home to give to his brother. how many marbles remain in Craig's collection?
Answers
Answer:
he would have 106
Step-by-step explanation:
hope it helps
write an equation in slope intercept form that passes through the given point and is perpendicular to the graph of given equation (1,-2) y=5x+4
Answers
The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.
The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.
To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.
The negative reciprocal of 5 is -1/5.
Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting the values:
y - (-2) = (-1/5)(x - 1)
Simplifying:
y + 2 = (-1/5)(x - 1)
To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:
y + 2 = (-1/5)x + 1/5
Subtracting 2 from both sides:
y = (-1/5)x + 1/5 - 2
Combining the constants:
y = (-1/5)x - 9/5
Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
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Beth has 44 extra N95 masks and she wants to distribute them among her 77 dearest friends, with each receiving at most one mask. In how many ways this can be done?
Answers
We want to see in how many ways we can divide 4 masks into 7 persons. We will see that the masks can be distributed in 35 different forms.
Finding the combinations.
Notice that this is equivalent to seeing how many different groups of 4 friends we can take from the group of 7 persons.
Remember that if we have a set of N elements, the total number of groups of K elements that we can take from that set is:
\(c(N, K) = \frac{N!}{(N - K)!*K!}\)
We can use that formula with N = 7 and K = 4, so we get:
\(c(7, 4) = \frac{7!}{(7 - 4)!*4!} = \frac{7*6*5}{3*2} = 35\)
So the masks can be distributed in 35 different forms.
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A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Answers
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
Point-slope form of the line that passes through (-8,2) and is perpendicular to a line with a slope of -8
Answers
Answer:
y-2=1/8(x+5)
Step-by-step explanation:
1. Perpendicular lines have opposite slopes. To get the new slope, take the slope of the first line and turn it to make it the opposite reciprocal.
Since it's -8, the opposite of it is 1/8.
2. Now, use point slope: y-y1=m(x-x1). Plug in the values of the ordered pair and the slope into the equation.
y-2=1/8(x+8)
And that's your answer
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answers
Answer:
a
Step-by-step explanation:
the perimeter (P) of a square is the sum of the 4 congruent sides.
the area of a square is calculated as
area = s² ( s is the length of a side )
here area is 36 , then
s² = 36 ( take square root of both sides )
s = \(\sqrt{36}\) = 6
then
P = 4s = 4 × 6 = 24 cm
Solve 3x-9 = 6.A. x = 2B. x=-1C. x = 1D. x = 5
Answers
Step 1. The expression that we have is:
\(3x-9=6\)And we need to solve for x.
If we are going to solve for x, we need to have the 'x' alone on one side of the equation.
For that, the first step is to add 9 to both sides:
\(3x-9+9=6+9\)Step 2. On the left side, -9+9 cancel each other, and on the right side 6+9 is 15:
\(3x=15\)Step 3. The next step is to divide both sides by 3:
\(\frac{3x}{3}=\frac{15}{3}\)In this way, 3/3 on the left side cancel each other and we are left only with x:
\(x=\frac{15}{3}\)And on the right side, 15/3 is equal to 5:
\(\boxed{x=5}\)This is shown in option D.
Answer:
D. x=5
a pyramid has a height of 5 inches and a volume of 60 cubic inches ?
Answers
Answer:
36 square inches.
Step-by-step explanation:
volume is given by 1 by 3, into base into height is based. His height and volume and area of the base is given by area of the ashe area of the base is given by 3 into 60 by 5. As given in the question on solving it, we get it equals to 36 square inches.
Distribute and simplify these radicals.
√12 (-1+√5)
-4√3
-2√3+2√15
4√3
6√3
Answers
The simplified expression of √12 (-1+√5) is -2√3 + 2√15
How to simplify the radical expression?The radical expression is given as:
√12 (-1+√5)
Express √12 as 2√3
So, we have:
√12 (-1+√5) = 2√3(-1+√5)
Evaluate the product
√12 (-1+√5) = (-2√3+2√15)
Remove the bracket
√12 (-1+√5) = -2√3 + 2√15
Hence, the simplified expression of √12 (-1+√5) is -2√3 + 2√15
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The distance from the base of a flagpole to a point on the ground is 24 feet. The flagpole has a height of 18 feet, as shown in the diagram below. Flagpole 18 feet Ground 24 feet What is r, the distance from the top of the flagpole to the point on the ground? A 16 feet B 21 feet C. 30 feet D. 42 feet
Answers
Answer: 30 feet
Explanation:
Given:
To find the distance from the top of the flagpole to the point on the ground, we use Pythagoras' Theorem.
\(a^2+b^2=c^2\)So, we plug in what we know
\(\begin{gathered} a^2+b^2=c^2 \\ (18)^2+(24)^2=(x)^2 \\ \text{Simplify and Rearrange} \\ 324+576=x^2 \\ x^2=900 \\ x=\sqrt[]{900} \\ \text{Calculate} \\ x=30 \end{gathered}\)Therefore, the distance from the top of the flagpole to the point on the ground is 30 feet.
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10 degrees to the horizontal. Calculate the length of the zip wire.
∘
to the horizontal. Calculate the length of the zip wire
Answers
The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.
To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.
Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).
The formula for sine is:
sin(angle) = opposite / hypotenuse
Rearranging the formula, we have:
hypotenuse = opposite / sin(angle)
In this case, the opposite side is the vertical distance, which is h.
So, the formula becomes:
hypotenuse = h / sin(angle)
To find h, we can use the formula for the length of the zip wire:
h = 25 * tan(angle)
Substituting this into the previous formula, we get:
hypotenuse = (25 * tan(angle)) / sin(angle)
Calculating the value, we have:
hypotenuse = (25 * tan(10°)) / sin(10°)
Using a calculator, we find:
tan(10°) ≈ 0.1763
sin(10°) ≈ 0.1736
Substituting these values, we can calculate the length of the zip wire:
hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters
Therefore, the length of the zip wire is approximately 25.35 meters.
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Solve the Inequality 3(х + 1) + 2(x + 2) > 0.
Answers
Answer:
5× + 7 > 0
Step-by-step explanation:
3(x + 1) + 2 ( x + 2) >0
3x + 3 + 2x + 4 > 0
5x + 7 > 0
You invest 1,000 in one account and 4,000 in another, both accounts have the same interest rate over the same amount of time. How will the interest earned compare?
Answers
Answer:
the $4000 WILL EARN 4 TIMES THE AMOUNT OF INTEREST.
Step-by-step explanation:
If both investments have same interest they will grow in the same proportion that the initial amount have.
10 points || answer ASAP if you can
Answers
Answer:
It would affect the mean, range, and standard deviation
Step-by-step explanation:
I got this right on the test :)
The table shows three unique, discrete functions.
x f(x) g(x) h(x)
-1
0
3
185
15
2
3
0
-25
-10-204
2
3
2
-3
2
3
4
5
6
Which statements can be used to compare the
characteristics of the functions? Select three options.
Of(x) has the greatest maximum.
h(x) has the greatest x-intercept.
g(x) has the smallest minimum value.
All three functions share the same domain.
All three functions share the same y-intercept.
Answers
All thre functions share the same y intercept
We can analyze the characteristics of the given functions based on the information provided in the table.
We cannot determine which function has the greatest maximum based on the table alone, as we do not have the complete graph of any of the functions.
We can see from the table that h(x) has an x-intercept of 0, which is the smallest among the three functions. Therefore, we can say that h(x) has the smallest x-intercept.
We can see from the table that g(x) has a minimum value of -204, which is the smallest among the three functions. Therefore, we can say that g(x) has the smallest minimum value.
We cannot determine if all three functions share the same domain based on the table alone. We can only see that all three functions have been evaluated at the same set of input values.
We can see from the table that the y-intercept of f(x) is 2, the y-intercept of g(x) is 3, and the y-intercept of h(x) is 4. Therefore, we can say that all three functions have different y-intercepts.
Therefore, the statements that can be used to compare the characteristics of the functions are:
h(x) has the smallest x-intercept.
g(x) has the smallest minimum value.
All three functions have different y-intercepts.
Is there a way to calculate this question using a scientific calculator?
Answers
Solution
For this case we know that:
\(\sec \theta=2\)Using the definition of sec we have this:
\(\frac{1}{\cos \theta}=2\)Then solving for cos we got:
\(\cos \theta=\frac{1}{2}\)Then the angle is :
\(\theta=arc\cos (\frac{1}{2})=\frac{\pi}{3},-\frac{\pi}{3}\)Then the answer is:
pi/3, -pi/3
Find the Area of the figure below, composed of a parallelogram and two semicircles. Round to the nearest tenths place.
Answers
Step-by-step explanation:
the total area = the area of full circle + the area of parallelogram = (π ×(8/2)²) + (28×7)
= (3,14 ×16)+(196)
= 50,24 +196
= 246,24
= 246,2
A ketchup company regularly receives large shipments of tomatoes. For quality control purposes, they take a sample of tomatoes from each shipment. If the sample shows convincing evidence that more than 8\%8%8, percent of the tomatoes in the entire shipment are bruised, then the company will request a new shipment of tomatoes. So the company tests H0 : p = 0.08 versus Ha : p > 0.08H, where p is the proportion of tomatoes in the entire shipment that are bruised.
One day, a supervisor takes a random sample of 600 tomatoes from a shipment and finds that 53 of the tomatoes are bruised, which results in a test statistic of z ≈ 0.75. Assuming that the necessary conditions are met, what is the approximate P-value associated with the significance test for this shipment?
Answers
Answer:
The value is \(p-value = 0.22663\)
Step-by-step explanation:
From the question we are told that
The proportion of bruised tomatoes p = 0.08
The null hypothesis is \(H_o : p = 0.08\)
The alternative hypothesis is \(H_a : p > 0.08\)
The sample size is n = 600
The number of bruised tomatoes from the sample selected is k = 53
The test statistics is z =0.75
Generally the p-value is mathematically represented as
\(p-value = P(Z > z)\)
=> \(p-value = P(Z > 0.75)\)
From the z-table
\(P(Z > 0.75) = 0.22663\)
So
\(p-value = 0.22663\)
Answer:
P-value ≈ 0.2266
Step-by-step explanation:
Expand (x-y)3 using Pascal triangle
Answers
Answer:
To expand (x-y)³ using Pascal’s triangle, we can write:
1
1 1
1 2 1
1 3 3 1
Each row of the triangle represents the coefficients of the binomial expansion of (a+b)ⁿ, with the top row being n=0.
So for (x-y)³, we take the fourth row of the triangle (starting with n=0), and substitute x and y into the formula, alternating the signs of y:
1x³ + 3x²(-y) + 3x(-y)² + 1(-y)³
= x³ - 3x²y + 3xy² - y³
Thus, (x-y)³ = x³ - 3x²y + 3xy² - y³.
Two times the sum of a number and 8 is negative 48 what is the number?
Answers
Answer:
-32
Step-by-step explanation:
Let the number be x.
\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)
im a senior trying to graduate my school has me in the wrong classes i have adhd and i was supposed to be in diffrent classes but anyways i need help bad its due tn at 12 and if i dont get them in i dont graduate
Answers
Step-by-step explanation:
hope you can send the questions again because your question is to long to answer everything. I answered 1,2,3,4
If p represents “a number is divisible by 2,” q represents “a number is odd,” and r represents “a number is even,” what does this statement imply?
WILL MARK BRAINLIEST!!!!
Answers
Answer:
B
Step-by-step explanation:
idk y but still ur teacher can't do anything
on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
Answers
The day and time that Thereas should take her 7th dose, given that she should take the dose every 12 hours is 9 am on Thursday.
How to find the day to take the dose ?From the first day that Therease took the dose which was 9 am on Monday, the table to show the days and times she takes the other doses, based on her taking them every 12 hours is:
Day Time
First dose Monday 9 am
Second dose Monday 9 pm
Third dose Tuesday 9 am
Fourth dose Tuesday 9 pm
Fifth dose Wednesday 9 am
Sixth dose Wednesday 9 pm
Seventh dose Thursday 9 am
Therese will therefore take the seventh dose at 9 am on Thursday.
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Help meee
this question
Answers
Answer:
1/6
Step-by-step explanation:
I dunno, I put this into a calculator and that's the answer it gave me.
Angles R and S are supplementary angles. which is the measure of R?
Answers
Answer:
R = 15°Step-by-step explanation:
Since angles R and S are supplementary angles it means that the sum of their angles add up to 180°
To find R we must first find x
To find x , add angles R and S and equate them to 180
That's
R + S = 180
80 - x + 3x - 30 = 180
2x + 50 = 180
2x = 180 - 50
2x = 130
Divide both sides by 2
x = 65°
From the question
R = 80 - x
But x = 65°
Substitute the value of x into the expression
That's
R = 80 - 65
We have the final answer as
R = 15°Hope this helps you
OPEN ENDED QUESTION
Does she have enough? She already used
60° and 75º. Use what you know about
the number of degrees in a circle to
determine whether or not she can draw a
200° angle with what is left.
I
Answers
Answer:Yes she can.
Step-by-step explanation:well a circle is 360 degrees and she has already used 60 and 75 degrees so 360-60-75= 225 degrees so yeah, she can still draw a 200 degree angle.
Please help me with this math question
Answers
Find the complete factored form of the
polynomial :
-8m²n-7m² nª
Enter the correct answer.
Answers
The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).
To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:
-8m²n - 7m²n = (-m²n) (8 + 7a)
Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.
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