Answer:
They bought 6 vanilla wafers and 21 chocolate, they add up to 27.
x = amount of vanilla wafers
y = amount of chocolate wafers.
4x+y = 45
x+y= 27
Step-by-step explanation:
x = amount of vanilla wafers
y = amount of chocolate wafers
Vanilla wafers = 4$ each
Chocolate wafers = 1$ each.
So, 4x+y = 45 and x+y= 27 because they spent 47$ on 27 packs.
With both equations we can substitute.
1. Change one equation so one variable is on one side
x+y = 27 to y = 27-x
2. Substitute the variable from the other equation.
4x+y = 45 to 4x+27-x = 45
3. Solve the equation for x.
4x+27-x = 45
3x+27 = 45
3x = 18
x = 6 (amount of vanilla wafers)
4. substitute with equation.
y = 27-x to y = 27-6
5. Solve the equation for y.
y = 27-6
y = 21 (amount of chocolate wafers)
A doctor claims that the mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night. To investigate, he selects a random sample of 50 high school seniors from all high schools in his county. He also selects a random sample of 50 seniors from the colleges in his county. He constructs a 95% confidence interval for the true mean difference in the number of hours of sleep for seniors in high school and seniors in college. The resulting interval is (0.57, 1.25). Based upon the interval, can the doctor conclude that mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night?
yes because 1 is in the confidence interval
yes because 0 is not in the confidence interval
no because 1 is in the confidence interval
no because 0 is not in the confidence interval
Considering the given confidence interval, the correct option regarding the conclusion of the hypotheses test is given by:
yes, because 0 is not in the confidence interval.
What are the hypotheses tested?At the null hypotheses, it is tested if the difference is equals to zero, that is:
[tex]H_0: \mu = 0[/tex].
At the alternative hypotheses, it is tested if it is different, hence:
[tex]H_1: \mu \neq 0[/tex].
The confidence interval is (0.57, 1.25). Since it does not contain 0, there is enough evidence that the difference is different of 0, hence the correct option is given by:
yes, because 0 is not in the confidence interval
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If cos43=p, determine.without the use of a calculator,the value of each of the following in terms of p
We need to calculate the value of cos(43) to determine the value of p
How to evaluate the expression?The equation is given as:
cos43 = p
Rewrite properly as:
cos(43) = p
Rewrite the equation as:
p = cos(43)
The above means that we simply calculate the value of cos(43) to determine the value of p
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How long will it take to triple a sum of money if it is invested at a rate of 6.25% compounded continuously? Round your answer to 2 decimal places.
Answer:
So the answer is approximately 18 years
Step-by-step explanation:
Your interest rate is 6.25%, or, 0.0625
A=P⋅(1+(r/n))^nt
Where:
P is the initial amount
r is annual rate of interest
t is number of years
A is the final amount of money
n is the number of times the interest is compounded per year
So
3P=P(1+0.0625)
3P=P (1.0625)^t
3=1.0625^t
Now we should use logarithmic functions.
ln(3)=t⋅ln(1.0625)
ln(3)ln(1.0625)=t
t=18.12 years
To rationalize a denominator that has more than one term, you multiply the
fraction by B+ B, where B is the conjugate of the denominator.
Answer:
False.
Explanation:
To rationalize a denominator that has more than one term, you multiply the fraction by [tex]\frac{b}{b}[/tex], where "b" is the conjugate of the denominator not the numerator.
false
you multiply both the denominator and the numerator not just the fraction.
This is very confusing to me
Answer:
the system is inconsistent
also ,Check the attached graph
Step-by-step explanation:
let D₁ be the line of equation 3x - 9y = 36
D₂ be the line of equation 2x - 6y = -8
In order to graph D₁ we need to find two point shot that lie on it.
→ If x = 0 , 3(0) - 9y = 36 ⇔ -9y = 36 ⇔ y = -4
Then the point C(0 , -4) lies on D₁
→ If x = 3 , 3(3) - 9y = 36 ⇔ -9y = 27 ⇔ y = -3
Then the point D(3 , -3) lies on D₁
Therefore,
D₁ is the line that connects the points C and D
Similarly,We can prove that the point she A(-4 , 0) and B(-1 , 1) lie on D₂
Then D₂ = (AB)
After graphing, we notice that D₁ and D₂ are parallel and they don’t have any point in common.
Therefore ,we say that’s the system is inconsistent
Bao owns a small business selling used books. She knows that in the last week 60 customers paid cash, 3 customers used a debit card, and 27 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a fraction in simplest form.
Answer:
It would be a 3/10 or 30% chance.
Answer:
Step-by-step explanation:
3/10 or .30 or30%
Tge length of the front page is 30 centimeters and the width is 20 centimeters the side length picture is 7 centimeters
Answer:
A model of a shopping centre is drawn to scale where 1 cm on the model represent 4 m on the ground. Music shop Thabo's Sports Ware Fati's Clothing shop Grocery store PARKING Coffee shop Toilets Restaurant Shoe store Physiotherapy Health and Fitness center 1.1 Which shop is on the right of the physiotherapy? (2) 1.2 Describe the position of the Coffee Shop in relation to the Toilets. (2)
y=-x-3
y=4x-5
2x-y=-2
x+y=4
3x+4y=-12
Y'ALL I NEED SOME SERIOUS HELP, ANYBODY KNOW THE ANSWERS?
Answer: Heyaa! :)
1. y=-x-3 = -1Slope: −1
y-intercept: (0,−3)
2. y=4x-5 = 4Slope: 4
y-intercept: (0,−5)
3. 2x-y=-2 = 2Slope: 2
y-intercept: (0,2)
4. x+y=4 = 1Slope: −1
y-intercept: (0,4)
5. 3x+4y=-12 = - 3/4Slope: −3/4
y-intercept:
(0,−3)
Hopefully this helps you!
- Matthew
How do you find x in this question?
Answer:
x = 70°
Step-by-step explanation:
The relevant relations are ...
base angles of an isosceles triangle are congruentconsecutive interior angles where parallel lines meet a transversal are supplementary__
Triangle OBQ is isosceles, so angle OQB = 40°. Triangle OPQ is isosceles, so angle OQP is x. The sum of angles OQB and OQP is angle BQP, which is supplementary to angle OPQ. That is, ...
(40° +x) +x = 180°
2x = 140° . . . . . . subtract 40°
x = 70° . . . . . . divide by 2
_____
There are many ways to find x. The one shown here is just one of them. In general, right triangles, isosceles triangles, symmetry, inscribed angles can all be used to write relations involving the known angles and x.
Subtract;
233.66-66.24
43.12-21.11
24.6-19.777
Answer:
1. 167.42
2. 22.01
3. 4.83
233.66-66.24 = 167.42
43.12-21.11 = 22.01
24.6-19.777 = 4.823
A pane of antique glass has dimensions of 30cm x 56cm. If the glass sells for 25 cents per square cm, what is the cost of the pane?
Given :-
Dimensions of pane is 30cm×56cmCost of pane per square cm is 25 centsTo find :-
Cost of the paneSolution:-
Hey mate , to find the total cost of pane we have to find the area of pane and multiply it by 25 cents
Area of pane :- 30×56cm²
Area of pane :- 1680cm²
Cost of pane :- 1860×25 cents
Cost of pane :- 42000 cents or 420$
Can anyone please solve this for me right now?
The width of the path when the length of the outer rectangle is 26+2x and width of it is 18+2x is 4 meters.
What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
A=a×b
Here, (a)is the length of the rectangle and (b) is the width of the rectangle
The length of the outer rectangle is 26+2x and width of it is 18+2x. The area of this rectangle is 884² m. Thus,
A=a×b
884=(26+2x)×(18+2x)
884=468+52x+36x+4x²
4x²+88x-416=0
Divide both side with 4,
x²+22x-104=0
x²+26x-4x-104=0
x(x+26)-4(x+26)=0
(x+26)(x-4)=0
x=-26,4
Take the positive value 4. The width of the path is equal to x which is 4 meters.
Hence, the width of the path when the length of the outer rectangle is 26+2x and width of it is 18+2x is 4 meters.
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A box is filled with 5red crayons, 9blue crayons, and 6yellow crayons.
A crayon is chosen at random from the box. Find the probability that it is a red or a blue crayon.
Write your answer as a fraction in the simplest form.
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
P(R or B)=[tex]\frac{5}{20}+\frac{9}{20}[/tex]
=[tex]\frac{7}{10}[/tex]
please do answer:
Simplify the expression---5x-2y + 3x + 2y
(100 points)
Combine like terms
5x+3x-2y+2y(5+3)x+(-2+2)y8x+08xAnswer:
8x
Step-by-step explanation:
Given expression:
[tex]5x - 2y + 3x + 2y[/tex]As we know, any negative integer being added by itself is 0. [-2y + 2y = 0]
[tex]\implies 5x - 2y + 3x + 2y[/tex][tex]\implies 5x + 3x + 0[/tex]Collect like terms and simplify;
[tex]\implies 5x + 3x + 0[/tex][tex]\implies x(5 + 3) + 0[/tex][tex]\implies x(8) + 0 = \boxed{8x}[/tex]Therefore, 8x is the simplified term.
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∆ABC is mapped to ∆A'B'C' using each of the given rules in the table below. Place a checkmark in the correct column for each mapping to state if the resulting mapping would make ∆ABC congruent or not congruent to ∆A'B'C'.
∆ABC is congruent to ∆A^' B^' C'
∆ABC is NOT congruent to ∆A^' B^' C'
(x,y) → (x+5,y)
(x,y) → (5x,5y)
(x,y) → (.5x,.5y)
(x,y) → (x,-y)
(x,y) → (-x,-y)
For reference you can look at the attachment
I have taken three points (1,1),(2,1),(3,3)Then converted them accordingly
#1(Graph 2)
Yes#2(Blue dots on graph 1)
NoThey are similar but not equal
#3(Purple dots)
NoSimilar but not equal
#4(Green dots)
Yes#5(Black dots)
YesDetermine all missing angles below.
Answer:
a = 60, b = 19, c = 101, d = 79, e = 50
Step-by-step explanation:
Relations that are helpful here are ...
vertical angles are congruentan exterior angle is equal to the sum of the opposite interior anglesthe sum of angles forming a straight angle is 180°the sum of angles in a triangle is 180°__
Using these relations, we can find the unknown measures.
a° = 60° . . . . . these are vertical angles
51° +b° +110° = 180° ⇒ b° = 180° -161° = 19° . . . . straight angle
a° +b° +c° = 180°
c° = 180° -60° -19° = 101° . . . . sum of angles in a triangle
d° = 180° -101° = 79° . . . . . straight angle
e° = c° -51° = 50° . . . . . c° is exterior to the triangle
Hello, help me please with explanation)
Answer:
hope this will help you sorry if the answer is wrong
please help me do my mathematics assignment experts
Step-by-step explanation:
try this option, note: 1) task 'd' is solved only; 2) the answer is marked with green colour.
a line passes through the point (-9,1) and has a slope of 4/3. Write an equation in slope-intercept form for this line.
Answer: y=4/3x+1
Step-by-step explanation:
The formula is Y=mx+b
b is the y-intercept and MX is slope
If l is parallel to m in the following figure, find the measure of x
Check the picture below.
Can someone please solve this for me using that method thank you I give brainliest
Identify the range of the function shown in the graph
Answer:
0 ≤ y ≤ 8
Step-by-step explanation:
DOMAIN is x values of a function/graph
RANGE is the y-values that a function can have .....
this one goes from 0 to 8 inclusive
A race course is 26.2 miles long. Of the entire race course, 5% is uphill. How many miles of the race course are uphill?
Answer:
1.31 miles of the race course are uphill
Step-by-step explanation:
Divide 5 × 26.2 miles by 100 and you'll get 1.31 miles.
Hope this helped :)
What is the length of the two equal sides?
What is the length of the third side?
Answer:
Two equal sides: 15 centimeters, Third side: 21 centimeters
Step-by-step explanation:
Sorry If I'm late, so how I solved this was by using variables and algebra. The perimeter of a triangle is the sum of all three sides. Let's now break down the problem and use the useful information, we know that the perimeter is 51 centimeters, and that there are two equal sides and the third side is 6 inches longer than the two equal sides. So it is pretty much an isosceles triangle since it has two sides of equal length and the third side is not equal to the others. So we can make an equation with variables. 51(Perimeter)=x(first equal side)+x(second equal side)+x(third side)+6(The third side is 6 centimeters longer than the two other sides), now we simplify the equation just like we do with most algebraic equations. x+x+x can be turned into 3x. This now makes the equation 51=3x+6, we can subtract 6 from both sides to just have the variable on one side, 3x+6-6, both sixes cross out making it 3x, 51-6 is equal to 45. Now we divide by three on both sides to give just x and find out what x is. 3x/3=x and 45/3=15. x=15, x is the equal side length, so the two equal sides are 15 centimeters and the third one is 21 centimeters. The reason for this is because 15+6=21. I hope this helped with your learning, if I am wrong please tell me :)
Compare 4 and -2. Which of the following is true?
Answer:
Your answer is A.
Step-by-step explanation:
Absolute values of any number are positive.
|4| = 2
|-2| = 2
2 = 2 and 4 > -2
C and D can be true, but they are not since less than or greater than doesn't apply if they were less than/greater than or equal, then yes.
what is the measure of BDC?
Find the slope of a line parallel to -3x+7y=-15
Answer:
[tex] \boxed{\rm \: Slope = 3/7 \: x}[/tex]
Step-by-step explanation:
Given :
3x+7y=-15To Find:
The slopeSolution:
Well,to find out the slope of the line here, we'll need to re-write the fully solved equation into slope - intercept form.
[tex] \boxed{ \rm \: y = mx = b}[/tex]
Here,
m = slopeb = y - intercept.[Add 3x to both sides to the original equation:]
[tex] \rm \: 7y = - 15 + 3x[/tex]Divide each term in this equation by 7:
[tex] \cfrac{7y}{7} = \cfrac{ - 15}{7} + \cfrac{3x}{7} [/tex][tex] \rm \: y = \cfrac{ - 15}{7} + \cfrac{3x}{7} [/tex]Now rewrite this equation into slope-intercept form.
[tex]y = mx + b[/tex]Plug values.
[tex]y = \cfrac{3x}{7} - \cfrac{15}{7} = \cfrac{3}{7} x - \cfrac{15}{7} [/tex] > So , y - intercept is 15/7> Slope m is 3/7 x.Hence,we can conclude:
The slope of the line parallel to -3x+7y=-15 is 3/7 x.[tex] \rule{225pt}{2pt}[/tex]
Which table of values was used to create the scatterplot below? A graph titled Fundraiser Amounts has Day of Fund Drive on the x-axis and Money Raised (dollars) on the y-axis. Points are at (1, 200), (2, 300), (3, 200), (4, 400), (5, 300). A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 400, 200, 300. A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 200, 300, 400. A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 200, 400, 300. A 2-column table with 5 rows. Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 200, 300, 400, 300.
The table of values used to create the scatterplot below is:
Column 1 is labeled Day of Fund Drive with entries 1, 2, 3, 4, 5. Column 2 is labeled Money raised (dollars) with entries 200, 300, 200, 400, 300
Which table of values was used to create the scatterplot below?The graphs x axis represents the Day of Fund Drive and y axis represents Money Raised.
The ordered pairs from the plot are:
(1, 200), (2, 300), (3, 200), (4, 400), (5, 300)
Therefore, the table of values used to create the scatterplot below will be:
Day of Fund Drive Money raised (dollars)
1 200
2 300
3 200
4 400
5 300
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Answer:
C.
Step-by-step explanation:
Edge 2023
Find the volume of a bird seed box with the following dimensions:
h = 26 cm
W = 10 cm
I = 17.5 cm
Please show work and thank you
Answer:
x = 6
Step-by-step explanation:
A 45-45-90 isosceles right triangle has side lengths in the ratios ...
1 : 1 : √2
__
That is, the longest side (marked x in this figure) is √2 times the length of the other two equal-length sides.
x = (√2)×3√2 = 3×2
x = 6