Given :
The 8 grade class is selling pennants and flags.They earn $1 for each pennantsold and $6 for each flag sold. They sell 50 items and earn $115.To Find :
How many pennants and how many flags did they sell?Solution :-
Let us take that ,
→ number of flags sold = f
→ number of pennant sold = p
Money earned by selling flags
→ Money = $6 * f = $6f
Money earned by selling pennants
→ Money = $1*p = $1p
Total money earned
→ Total Money = $6f + $1p
Total items sold
→ Total items = f + p = 50 . . . . . (i)
According to the question ,
→ 6f + p = 115 . . . . . (ii)
Solving equations (i) and (ii) ,
On subtracting them ,
→ 6f - f = 115 -50
→ 5f = 65
→ f = 65/5
→ f = 13
Substitute this in equation (i) ,
→ 13 + p = 50
→ p = 50 -13 = 37
Hence they sold 13 flags and 37 pennants .
I hope this helps .
A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects 10 cans at random, measures their contents, and computes a 95% confidence interval for the true mean volume. For one particular hour, the 95% confidence interval is 11.97 ounces to 12.05 ounces.
a. Does the confidence interval provide convincing evidence that the true mean volume is different than 12 ounces? Explain your answer.
b. Does the confidence interval provide convincing evidence that the true mean volume is 12 ounces? Explain your answer.
According to the given confidence interval, we have that:
a) Since 12 ounces is part of the confidence interval, the interval does not provide convincing evidence that the true mean volume is different than 12 ounces.
b) Since 12 ounces is part of the confidence interval, the interval provides convincing evidence that the true mean volume is 12 ounces.
What is the hypothesis tested?It is being tested if the true mean volume is different of 12 ounces, hence:
If the confidence interval contains 12 ounces, it provides convincing evidence that the true mean volume is 12 ounces.If the confidence interval does not contain 12 ounces, it provides convincing evidence that the true mean volume is not 12 ounces.In this problem, the interval is (11.97, 12.05), hence it provides convincing evidence that the true mean volume is 12 ounces, and basically, item a is False and item b is True.
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C. Multiple Choice. Read each Item Carefully. Choose the letter of the correct answer then write it on the
space provided for. (Use figures 1, 2 and 3 for item #s 11-15.)
figure 1 figure 2 figure 3
___________11. What is the side corresponding to PO in ΔPOG ≅ ΔSOR (figure 1)?
A. OS B. RD C. RS D. SO
____________12. Name the congruent triangle illustrated in figure 1
A. ΔFOG ≅ ΔSOR B. ΔPOG ≅ ΔROS C. ΔROS ≅ GOS D. ΔPOR ≅ ΔGOS
____________13. What is the triangle congruence postulate used in figure 2 based on its marking.
A. SSS postulate B. ASA Postulate C. SAS Postulate D. AAA postulate
____________14. Based on the given marking in figure 3, what is the triangle congruence postulate is used in
describing triangle.
A. SSS postulate B. ASA Postulate C. SAS Postulate D. AAA postulate
___________15. In figure 3, If triangle ΔABC ≅ ΔXYZ. What is the congruent angle of ∠A?
A. ∠B B. ∠X C. ∠Z D. ∠B
Congruent triangles have congruent corresponding sides and angles, while similar triangles may or may not be congruent
Corresponding side of POThe congruence statement is given as:
ΔPOG ≅ ΔSOR
The above means that:
Points P, O and G correspond to the points S, O and R
Hence, the corresponding side of PO in ΔPOG ≅ ΔSOR is SO
The congruent trianglesThe congruence statement is given as:
ΔPOG ≅ ΔSOR
Hence, the congruent triangles are ΔPOG ≅ ΔROS
The congruent postulateIn figure 2, we have:
2 congruent sides, and 1 congruent angle between the congruent sides
Hence, the congruence postulate is SAS
Congruent anglesThe congruence statement is given as:
ΔABC ≅ ΔXYZ
The above means that:
Point A corresponds to the point X
Hence, the congruent angle of <A is <X
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Solve the following system of equations and show all work.
y = −x2 + 4
y = 2x + 1
PLEASE PLEASE HELP!!!!
Find the value of x.
6x°
60°
A. 20
B. 10
C. 15
D. 5
Answer:D
Step-by-step explanation:
D
Answer:
I think the answer is letter C.15
Correct me if im wrong
#Thank you
Triangle ABC is right triangle. The length of one leg is 80 centimeters, and the hypotenuse is 120 centimeters. What is the length, in centimeters, of the other leg?
The length of the other leg of the right triangle is; 89.44 centimetres
Right triangles and the Pythagoras theoremAccording to the question;
We are required to determine the length, in centimetres of the other leg of the right triangle.By the Pythagoras theorem;
Hyp² = Opp² + Adj²Hence, It follows that;
120² = 80² + X²x² = 14400-6400x² = 80,000Find the square root of both sides of the equation;
x = √80,000x = 89.44 centimeters
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Bob is throwing a party. He had 22 pints of soda. At the end of the party, there are 8 pints of soda. How many cups of soda were drank during the party?
Answer:
14 pints were drank
Step-by-step explanation:
22 pints - 8 pints =
Answer:
14 pints
Step-by-step explanation:
22 - 8 is 14 pints, now just convert the pints to cups, that would be 28 cups since 1 pint is 2 cups so 14 x 2 is 28, hope this helps
i need help with this
[tex] \frac{2}{3} + \frac{1}{6} [/tex]
please can you do it for me
[tex] \frac{5}{6} [/tex]
Given sin 0=7/4and angle 0 is in quadrant 1 what is the exact value of cos 0 in simplest form? Simplify all radics if needed
Answer:
Answer: ¾
Step-by-step explanation:
» From the trigonometric identities:
[tex]{ \tt{ \sin {}^{2} \theta + \cos {}^{2} \theta = 1 }}[/tex]
» Substitute to the formular:
[tex]{ \tt {( \frac{ \sqrt{7} }{4} )}^{2} + { \cos }^{2} \theta = 1 } \\ \\ { \tt{ \frac{7}{16} + { \cos}^{2} \theta = 1 }} \\ \\ { \tt{ \cos {}^{2} \theta = 1 - \frac{7}{16} }} \\ \\ { \tt{( \cos\theta) {}^{2} = \frac{9}{16} }} \\ \\ { \tt{ \sqrt{ {( \cos \theta}^{2}) } = \sqrt{( \frac{9}{16}) } }} \\ \\ { \tt{ \cos \theta = \frac{ \sqrt{9} }{ \sqrt{16} } }} \\ \\ { \boxed{ \tt{ \cos \theta = \frac{3}{4} }}}[/tex]
Use the following compound interest formula to complete the problem. A = P (1 StartFraction r over n EndFraction) superscript n superscript t Currently you have two credit cards, H and I. Card H has a balance of $1,186. 44 and an interest rate of 14. 74%, compounded annually. Card I has a balance of $1,522. 16 and an interest rate of 12. 05%, compounded monthly. Assuming that you make no purchases and no payments with either card, after three years, which card’s balance will have increased by more, and how much greater will that increase be? a. Card I’s balance increased by $53. 16 more than Card H’s balance. B. Card I’s balance increased by $13. 45 more than Card H’s balance. C. Card H’s balance increased by $35. 61 more than Card I’s balance. D. Card H’s balance increased by $49. 06 more than Card I’s balance. Please select the best answer from the choices provided A B C D.
Answer:
B. card I'' increased by 1.2986 = 13 more than card H's
Step-by-step explanation:
What is the quotient of 36,772 and 58?
Answer:
634.Step-by-step explanation:
Quotient meaning:
To divide 2 numbers.Equation:
36,772 ÷ 58Solve:
36,772 ÷ 58= 367 - 348 = 19= 197 - 174 = 23= 232 - 232= 0Multiples:
6, 3, and 4.Answer:
634.Answer:
634
Step-by-step explanation:
Help please! 50 points.
[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]
Here's the solution ~As we observe the points, we can conclude that :
Translation along x axis is ~
[tex]\qquad \sf \dashrightarrow \: 1 - ( - 3)[/tex]
[tex]\qquad \sf \dashrightarrow \:1 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \:4 \: \: units \: \: towards \: \: left[/tex]
Translation along y axis ~
[tex]\qquad \sf \dashrightarrow \: - 8 - ( - 13)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 8 + 13[/tex]
[tex]\qquad \sf \dashrightarrow \:5 \: \: units \: \: towards \: \: down[/tex]
So, same goes with translation of (-5 , 9)
[tex]\qquad \sf \dashrightarrow \: x \: \:coordinate = - 5 - 4 = - 9[/tex]
[tex]\qquad \sf \dashrightarrow \: y \: \:coordinate = 9 - 5 = 4[/tex]
So, the required coordinates of the image under same translation is ~
[tex]\qquad \sf \dashrightarrow \:(-9, 4)[/tex]
Answer:
Please help look at the image I need help with number 4. I already did the line plot for number 3 and the data in on the chart. Thank you! :)
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOO SCAMS PLEASE. Find the area of the figure
_____m squared
Answer:
11700 m²
Step-by-step explanation:
Split the shape in two. One rectangle 150x30 and one triangle 180x80.
Find the areas of both and add them:
A = bh + 1/2bh
A = 150(30) + 1/2(180)(80)
A = 4500 + 7200
A = 11700
Which set of ordered pairs (x,y) could represent a linear function
Pls help asap I will give brainliest
Answer:
the zeroes are -2 and 8
Step-by-step explanation:
[tex]-x^2 +6x+16\\\implies -(x^2-6x-16)\\\implies -(x+2)(x-8)[/tex]
Therefore, the zeroes are -2 and 8
Selena buys several shares of stock at $32 per share and sells them at $28. 32 per share. What is the percent of decrease in the price of the stock? 12. 0% 11. 5% 11. 0% 10. 5%.
The total percent of decrease in price of the shares of Selena's stock which Selena first buys and then sold is 11.5 percent.
What is percentage decrease?Percentage decrease in a number is the ratio of total decrease in the original value of a number to the decreased value in the percentage form.
Given information-
The total stock buy by the Selena in $32.
The total stock sold by the Selena in $28.32.
As the total stock buy by the Selena in $32, and the total stock sold by the Selena in $28.32. Thus the total decrease in the price of stock is,
[tex]C_s=32-28.32\\C_s=3.68[/tex]
Thus the total decrease in the price of stock is $3.68.
As the cost price of the stock is $32 and the total decrease in the price of stock is $3.68. Thus the total percent of decrease in the price of the stock is,
[tex]\Delta C_s=\dfrac{3.68}{32}\times100\\\Delta C_s=11.5[/tex]
Thus the total percent of decrease in the price of the stock is 11.5 percent.
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PLS HELP MARKING BRAINLEIST
Answer:
[tex]4p^2q-4q+8p[/tex]
Step-by-step explanation:
[tex](12p^2q+p-3pq^2)-(4q-7p+8p^2q-3pq^2)[/tex]
Apply rule [tex]-(-a)=a[/tex] and [tex]-(a)=-a[/tex]:
[tex]\implies 12p^2q+p-3pq^2-4q+7p-8p^2q+3pq^2[/tex]
Collect like terms:
[tex]\implies 12p^2q-8p^2q-3pq^2+3pq^2-4q+7p+p[/tex]
Combine like terms:
[tex]\implies 4p^2q-4q+8p[/tex]
what is the answer to 7864 ÷ 51
The quotient of a number and -7,
decreased by 2, is 10. Find the
number.
Answer:
-84
Step-by-step explanation:
Let the number be x. Then we have,
[tex]\frac{x}{-7}[/tex] (the quotient of a number and -7)
[tex]\frac{x}{-7}-2[/tex] (decreased by 2)
[tex]\frac{x}{-7}-2=10[/tex] (is 10)
Now we can solve for x,:
[tex]\frac{x}{-7}-2=10[/tex]
[tex]\frac{x}{-7}=12[/tex]
[tex]x=-84[/tex]
So, the original number is -84
Answer:
-84
Step-by-step explanation:
[tex]\frac{n}{-7}[/tex] -2 = 10
add 2 to each side to get:
[tex]\frac{n}{-7}[/tex] = 12
multiply each side by -7 to get:
n = -84
Eight times the sum of a number and 20 is less than 29
Answer:
8 • 20m - 29
Step-by-step explanation:
this might be right
Convert the following fraction into decimals by changing denominator of 7/5 a multiple of 10
Answer:
1.4
Step-by-step explanation:
= 7/5 × 2/2
= 14/10
=1.4
On a boat tour, there are half as many children as there are adults. How many children are there? There are 30 people on the tour.
Answer:
15 children
Step-by-step explanation:
30÷2
=15
therefore there is 15 adults and 15 children
Which of the following are exterior angles? Check all that apply.
Answer:
4 and 5
Step-by-step explanation:
A hand glider dives at 25 mph in a direction 60° below horizontal. What is the component form of the velocity vector?.
Velocity can be represented in horizontal and vertical components
The horizontal component form of the velocity is 12.5 mph
How to determine the component form of the velocityThe given parameters are:
Velocity = 25 mph
Angle = 60 degrees
The horizontal component form of the velocity is then calculated as:
[tex]v_x = 25 * \cos(60)[/tex]
Evaluate the product
[tex]v_x = 12.5[/tex]
Hence, the horizontal component form of the velocity is 12.5 mph
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HELP ILL MARK BRANLIEST
Rectangle CDEF is rotated 45° in a clockwise direction. To which angle of the image does angle D correspond?
angle C prime
angle D prime
angle C
angle D
Answer:
Angle C prime
Step-by-step explanation:
First design and sketch it:
Make a rectangle with corners C D E and F. 90 degrees each. Now rotate it 45 degrees to the left. Angle D is diagonally from Angle C.
I hope this helps! :)
I NEED HELP ASAP I NEED THIS IN 3 MINUTES I GIVE BRAINLEST
Answer:
-4
Step-by-step explanation:
(-12) - (-5) = -7
-7 + 3 = -4
Answer:
-4
Step-by-step explanation:
HOPE IT HELPED U
please help me with the question
Answer:
-2.5 m/s^2
Step-by-step explanation:
From 2 seconds to 8 seconds (the last 6 seconds), the speed decreased from 15 m/s to 0. The average acceleration is ...
(-15 m/s)/(6 s) = -2.5 m/s^2
2 more than 5 times a number is greater than or equal to 3
Answer:
x >= 1/5
Step-by-step explanation:
2 + 5x >= 3
5x >= 1
x >= 1/5
Which regions have populations with 9 as the power?
Answer:
the regions whose populations have 9 as the power include Africa and Asia.
Step-by-step explanation:
Answer:
africa and asia
Step-by-step explanation:
Type the correct answer in the box. The solubility of calcium carbonate is 14. This rate means that 14 milligrams of calcium carbonate can dissolve in 1 liter of water. How much water would be required to fully dissolve 11 grams of calcium carbonate? Express your answer to the correct number of significant figures. One milligram is equal to 0. 001 grams. It would take liters of water to fully dissolve 11 grams of calcium carbonate.
Ratio compares two quantities. The amount of water that will be needed to dissolve 14 grams of calcium carbonate is 1000 liters.
Given to us
The solubility of calcium carbonate is 14.
We know that to dissolve 14 milligrams of calcium carbonate we will need 1 liter of water. therefore, the ratio of water and calcium carbonate can be written as,
[tex]\rm \dfrac{calcium\ carbonate}{water} = \dfrac{14\ milligram}{1\ liter}[/tex]
We need to find the amount of water needed to dissolve 14 grams of water, therefore, we will convert grams to milligrams,
1 gram = 1000 milligram
14 gram = 14,000 milligram
Using the same ratio,
[tex]\rm \dfrac{14,000\ milligram}{water} = \dfrac{14\ milligram}{1\ liter}[/tex]
[tex]\rm {water} = \dfrac{14000\ milligram \times 1\ liter}{14\ milligram}[/tex]
water = 1000 liters
Hence, the amount of water that will be needed to dissolve 14 grams of calcium carbonate is 1000 liters.
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