(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
In the question ,
Part(1)
let the number of chocolates be "x" .
let the number of chocolates with covered almonds be "y"
price of each chocolate bar = $1.25
price of each chocolate covered almonds = $2
Beta club needs more than $375
So , according to the question
1.25x + 2y > 375
and also the students can sell up to 500 bars and covered almonds altogether.
So , x+y ≤ 500 .
Part(2)
Given , the club sells 100 chocolate bars.
substituting x= 100 in the inequality 1.25x + 2y > 375 , we get
1.25(100) + 2y > 375
125 + 2y > 375
2y > 375-125
2y > 250
y > 125
least number of chocolate covered almonds to be sold is 126 .
Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
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Can anyone solve this please, tommorow is my exam
Answer:
x=172°
Step-by-step explanation:
5x-11=3x-5
2x-11=5
2x=16
x=8
180-8=172
Finding Slope
HELP ME
Answer: slope is -3
Step-by-step explanation: (-5,6) and (-9,-6)
Take your Y values and subtract them -6-6=-12
Take your X values and subtract them -9-(-5) or -9+5= -4
Then your -12 will be your numerator and your -4 will be your denominator
Then Divide
-12/-4= -3
I hope this helps!
An observation deck extends 200 feet out above a valley. The deck sits 150 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by h=-16t^2 +150. How long will it take for the object to be 6 feet above the valley floor?
If equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds
The equation of the height h = -16[tex]t^2[/tex]+150
Where h is the height
t is the time taken
We have to find the time taken for the object to be 6 feet above the valley floor
The height = -150+6
= -144
Substitute the values in the equation
-16[tex]t^2[/tex]+150 = -144
-16[tex]t^2[/tex] = -144-150
-16[tex]t^2[/tex] = -294
[tex]t^{2}[/tex] = 18.375
t = 4.28 seconds
Hence, if equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds
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The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are less than 250 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places
For a random day with the standard deviation, the probability that there are less than 200 shoppers on a random day, is 0.0039.
The average total number of shoppers on a grocery store in 1 day is 506; the standard deviation is 115.
The number of shoppers is normally distributed.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 506 and standard deviation of 115.
Then, we can say that,
Z=(X-506)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P(X<200)
[tex]=P(Z < \frac{200-506}{115})[/tex]
=P(Z<-2.66)
Where, Z is the standard normal variate.
ρ = -0.266
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.0039
For a random day, the probability that there are less than 200 shoppers on a random day, is 0.0039.
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The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium -137 remaining after t years is given by the following exponential function.A (t) = 523 (1/2)^t/30Find the initial amount in the sample and the amount remaining after 100 years.Round your answers to the nearest gram as necessary.Initial amount:Amount after 100 years:
After 100 years:
Replace t by 100:
A (t) = 523 (1/2)^t/30
A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams
The initial amount of the sample is 523
Is (x-3) a factor of 2x^3 -4x^2-6?
1) (Type yes or no in the first blank)
2) What is the remainder?
(Type the answer in the second blank)
1. x - 3 is not a factor
2. The remainder is 32.
1. How to determine if x - 3 is a factor of 2x³ - 4x² - 6?Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.
So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then
p(3) = 0
So, substituting x = 3 into the equation, we have
p(3) = 2x³ - 4x² - 6
= 2(3)³ - 4(2)² - 6
= 2(27) - 4(4) - 6
= 54 - 16 - 6
= 54 - 22
= 32
Since p(3) ≠ 0.
x - 3 is not a factor
2. What is the remainder?Since p(3) = 32,
The remainder is 32.
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A ride sharing company offers two options: riding in small cars that can carry up to 3 passengers each, or riding in large vans that can carry up to 6 passengers each. A group of 27 people is going to use the ride sharing service to take a trip. The trip in a small car costs $10 and the trip in a large van costs $15. The group ends up spending $80 total.What do x and y represent?
Answer:
x = no of people in a small car
y = number of people in a van
Explanation:
The relevant information in the problem is that the total number of people is 27 and that the small car costs $10 and the large van $15.
If we call x the number of people in a small car, and y the number in the large van then the following equations can be obtained
[tex]\begin{gathered} x+y=27 \\ 10x+15y=80 \end{gathered}[/tex]The first equation simply says that the total number of people is 27 and the second equation says that the total cost of the trip is $80.
Hence,
x = no of people in a small car
y = number of people in a van
What is the solution to this equation?
5(x-3) = 21
A x =
OB x=
36
5
D x=
65
6
5
24
OC X= 5
18
5
Answer:
x = 7.2
Step-by-step explanation:
[tex]5(x - 3) = 21[/tex]
[tex]x - 3 = 4.2[/tex]
[tex]x = 7.2[/tex]
the measure of the angles of a triangle are shown in the figure below. solve for x
64°
x°
40°
Answer:
Sum of angles in a triangle add up to 180°.
x = 180 - 64 - 40
= 76°
Convert to Slope-Intercept Form3x + 4y = 4
The slope-intercept form generally can be represented as;
[tex]y\text{ = mx + c}[/tex]where m represents the slope and c is the y-intercept
So in this case, we have to make y the subject of the formula;
3x + 4y = 4 will be
4y = 4-3x
4y = -3x + 4
we now need to make y the subject of the formula;
[tex]\begin{gathered} \frac{4y}{4}\text{ = }\frac{-3x}{4}\text{ + }\frac{4}{4} \\ \\ y\text{ = }\frac{-3}{4}x\text{ + 1} \end{gathered}[/tex]which is true about box plots? group of answer choices boxplots show the number of datapoints between any two values boxplots present the shape of the distribution (density curve) boxplots can involve a categorical variable and a continuous numerical variable boxplots show the size of the data set (number of data points) boxplots visually present the mean and standard deviation boxplots show where the peak of the distribution is
Box plots present the shape of the distribution (density curve), Box plots can involve a categorical variable and a continuous numerical variable, Box plots show where the peak of the distribution is are the correct statement.
Instead of showing the raw data points, Box Plots takes the sample data and then present the ranges of values based on the quartiles and also display the asterisks for outliers that generally falls outside the whiskers.
Yes, the shape of distribution can be understood from a Box Plot. It can show whether a statistical data set is normally distributed or skewed.
A Box plot is a graph of the distribution that has Continuous variables. It is also applicable for Categorical variables.
Box Plot generally shows the below parameters: Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.
A size can be determined by using these parameters but is not directly seen in a Box Plot
Generally a Standard Deviation is not visualized by Box Plot. It mainly visualizes Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.
Yes, the peak of the distribution can be analyzed from Box Plot
Generally for Normal Distribution, Mean = Median and this is the point where the peak is seen.
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which hill's criteria, addressing whether the exposure comes before or after the effect, is the only criteria that must be met 100% for a causal relationship to be possible?
Hill's Criteria of Strength is the only criteria that must be met 100% for a causal relationship to be possible.
The Criteria of strength is Hill's first test for causation. He stated that the likelihood of an association being causative increases with the size of the connection between exposure and disease. Hill used Percival Pott's investigation into the prevalence of scrotal cancer in chimney sweeps to highlight this issue. Since the correlation between that occupation and sickness was so strong (almost 200 times more than in other jobs), it was concluded that chimney soot was probably a contributing factor. On the other hand, Hill argued that minor connections are less indicative of causation since they are more likely to be explained by other underlying factors (such as bias or confounding).
To evaluate possibly causative associations, it is essential to define what is meant by a "strong" correlation. Scientists may now distinguish between strong and weak associations using more mathematically sound criteria than Hill had in mind because of developments in statistical theory and computing capacity. Strength is no longer just understood as an association's magnitude. Furthermore, multi-factorial disorders and the existence of determinant risk variables that are tiny in magnitude but statistically significant have received more attention from researchers. The recognized standard for determining the strength of an observed correlation and, hence, its potential causation, is statistical significance today rather than the magnitude of the association.
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Product of two rational no. is 1 , if one of them is ⁵/², then the other no. isa) ⅖b) -1 c) 0
Given:
Product of two numbers is 1.
The one number is 5/2.
Let the another number be x.
[tex]\begin{gathered} x\times\frac{5}{2}=1 \\ x=1\times\frac{2}{5} \\ x=\frac{2}{5} \end{gathered}[/tex]Answer: Option a) is correct. the other number is 2/5.
What number should be subtracted from both sides of the following equation to solve for x?x + 27 = 303027573
Step 1
Given;
[tex]x+27=30[/tex]Required; To solve for x
Step 2
Add -27 to both sides
[tex]\begin{gathered} x+27-27=30-27 \\ x=3 \end{gathered}[/tex]Answer; The number that should be subtracted from both sides of the equation is 27
Stella needed to get her computer fixed. She took it to the repair store. The technician
at the store worked on the computer for 4 hours and charged her $59 for parts. The
total was $359. Which tape diagram could be used to represent the context if z
represents the cost of labor per hour?
Answer: 75 per hour
Step-by-step explanation:
A chemist is using 363 milliliters of a solution of acid and water. If 13.6% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
If 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
In the question;
it is given that
the total solution of acid and water is 363 milliliters .
and also it is given that 13.6% of the solution is acid ,
which means
the amount of acid in solution = 13.6% of total solution
Substituting the values , and
on solving further ,
we get
amount of acid in solution = 0.136×363 ......as 13.6% = 0.136
= 49.368
≈ 49.4 milliliter
Therefore , if 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
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Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?
9xy³-4y-10x2y2 + x³y + 3x² + 2x²y²-9y4
Answer:
I believe the answer is c
Step-by-step explanation:
You see, in a standard form the term with greater stays at the very right.
Use the given endpoint R and midpoint M of RS¯ to find the coordinates of the other endpoint S.
R(3, 0), M(0, 5)
Step-by-step explanation:
the midpoint coordinates between 2 points A and B are
((xa + xb)/2, (ya + yb)/2)
xa = 3
ya = 0
and so we get
(3 + xb)/2 = 0
3 + xb = 0
xb = -3
(0 + yb)/2 = 5
yb = 10
therefore, S = (-3, 10)
Last year, Milan had $10,000 to invest. He invested some of it in an account that paid 9% simple interest per year, and he invested the rest in an account that
paid 7% simple interest per year. After one year, he received a total of $780 in interest. How much did he invest in each account?
Answer:
$4000 at 9% and $6000 at 7%Step-by-step explanation:
Let the amount invested at 9% be x.
Then the amount invested at 7% is 10000 - x.
The amount of interest after one year is $780.
Set up equation to represent this:
0.09x + 0.07(10000 - x) = 7800.09x + 700 - 0.07x = 7800.02x = 780 - 7000.02x = 80x = 80/0.02x = 4000Amount invested at 7% is:
10000 - 4000 = 6000Answer:
Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.Step-by-step explanation:
Given information:
Total amount invested = $10,000.Account A = 9% simple interest per year.Account B = 7% simple interest per year. Total interest earned after one year = $780.Let x be the amount invested in Account A.
Therefore, the amount invested in Account B is (10000 - x).
Simple Interest Formula
I = Prt
where:
I = Interest earned.P = Principal invested.r = Interest rate (in decimal form).t = Time (in years).Create two equations using the given information:
[tex]\begin{aligned}\textsf{Interest: Account A} &= x \cdot 0.09 \cdot 1\\& = 0.09x\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Interest: Account B} &= (10000 - x) \cdot 0.07 \cdot 1 \\& = 0.07(10000 - x)\\& = 700-0.07x\end{aligned}[/tex]
As the total interest earned was $780, set the sum of the two found equations to 780 and solve for x:
[tex]\begin{aligned}\implies 0.09x+700-0.07x&=780\\0.02x+700&=780\\0.02x&=80\\x&=4000\end{aligned}[/tex]
Therefore, Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.Simplify -1(15+4 - 27) over 16
[tex] \frac{ - 1(15 + 4 - 27)}{16} \\ = \frac{ - 1(19- 27)}{16} \\ = \frac{ - 1( - 8)}{16} \\ = \frac{8}{16} \\ = 0.5[/tex]
ATTACHED IS THE SOLUTION
Answer:
= - 19 + 16^27
how to graph y=2x+2 please help
The graph of the equation is attached to the solution.
We can graph the equation of the line by finding the x and y intercept of the line.
We know that the equation is in the slope intercept form.
Hence, we can write the y-intercept of the line as 2.
The coordinates of the point will be (0,2).
To find the x - intercept, we can put y = 0
0 = 2x + 2
-2 = 2x
x = -2/2 = -1
x = -1
The coordinates of the point will be (-1,0).
We can find another point on the line.
Let x = 1
y = 2(1) + 2
y = 2 + 2
y = 4
The coordinates of the point will be (1,4).
We can plot these points on the graph and get our graph.
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14. A surveyor observes that the top of a building makes an angle of 32° with the road.From another location 300 ft. from the base of the building, the angle of elevation is 22°How far is the base of the building from the first observation point, ×, on the road?
Considering h as the height of the building, we have the following set of relations for a right triangle:
[tex]\begin{gathered} 300\cdot x=h^2 \\ h=300\cdot\tan22\degree \\ h\approx121\text{ ft} \\ \therefore x=\frac{121^2}{300}\approx49\text{ ft} \end{gathered}[/tex]Find the measure of
Answer: 93°
Step-by-step explanation:
[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]
The formula written in symbols as T =UN. Solve the formula for U.
The formula written in symbols as T =UN. Solve the formula for U.
we have
T=U*N
solve for U
so
isolate the variable U
step 1
divide by N both sides
T/N=U*N/N
T/N=U
therefore
U=T/Nwhat is the answer to 20x + 35y
The greatest common factor is 5 .
If you factor it out, the expression becomes 5 (4x + 7y) .
Answer: 55x^1 y^1
Step-by-step explanation:
Add 20+35= 55
x & y can't stand by it's self, so x^1 and y^1
So you take those answers and you got 55x^1 y^1
You must keep it in letters in alphabetic order or it's considered wrong.
Using the information in the diagram determine the height of the tree
Given
To find the height of the tree.
Explanation:
It is given that,
From the figure, it is clear that ΔABC and ΔADE.
That implies,
[tex]\begin{gathered} \frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC} \\ \frac{x}{2x}=\frac{y}{2y}=\frac{DE}{200} \\ \frac{1}{2}=\frac{DE}{200} \\ DE=\frac{200}{2} \\ DE=100 \end{gathered}[/tex]Hence, the height of the tree is 100ft.
Nicholas was the lucky journalist assigned to cover the Best Beard Competition. He recorded the contestants' beard colors in his notepad. Nicholas also noted if the contestants were signed up for the mustache competition later in the day. Only in the beard competition Also in the mustache competition Red beard 2 5 Grey beard 2 06 2 What is the probability that a randomly selected contestant has a red beard or is only in the beard competition? Sm out Simplify any fractions
Sample space n(s)=2+2+5+7=16
Let P(E) be the probability of red beard or is only in the beard competition:
Total number of red beard=2+5=7
P(red beard)=2/7
Theorems and Proofs problemIll send a picture of the question
According to the given information, the reason for the second statement is definition of supplementary angles, this is because the definition of supplementary angles says that the sum of two supplements is 180°.
It means that the answer is B. Definition of supplementary angles.
Expand 3(x - 1)(x + 4) and simplify.
Answer:
3x2-11x-4
Step-by-step explanation:
ross is camping 4 miles west and 11 miles north (-4,11)
Using the equation for the distance between two points, the distance between Ross and Rachel is given by the following option:
D. 19 miles.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, and the hypotenuse represents the distance between them.
Their coordinates in this problem are as follows:
Ross: (-4, 11).Rachel: (8, -4).Each unit on the plane represents a mile, hence their distance is given as follows:
[tex]D = \sqrt{(8 - (-4))^2+(-4 - 11)^2}[/tex]
D = 19.2 miles.
Rounded to 19 miles, hence option D is correct.
Missing informationThe complete problem is given by the image at the end of the answer.
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