Answer:
100
Step-by-step explanation:
A bakery sells cakes for $23 and a dozen cupcakes for
$18. In one day they sold 72 items and made a total of
$1446. Which system is an appropriate model of the
problem?
A.23x + y = 72
18x+ y = 1446
B.x+y=72
23x18y=4600
C.23x + 18y = 72
x + y = 1446
D. 23x + y = 1446
x + 18y = 72
Answer:
23x + 18y = 1446
x + y = 72
Step-by-step explanation:
The bakery made $1446 total. We represent this as the cost of each cake ($23) times the number of cakes sold (x) plus the cost of each dozen cupcakes ($18) times the number of cupcakes sold (y).
Thus, 23x +18y = $1446.
The bakery sold 72 items total. We represent this as the number of cakes sold (x) plus the number of each dozen cupcakes sold (y).
Thus, x + y = 72.
A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.
Hey there! I'm happy to help out!
As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.
However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:
[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]
So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!
[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512
However, we want to find how much he has done in total! So, let's find how much he did on the other squares!
[tex]2^8[/tex]= 256
[tex]2^7[/tex]=128
[tex]2^6[/tex]=64
[tex]2^5[/tex]=32
[tex]2^4[/tex]=16
2³=8
2²=4
[tex]2^1[/tex]=2
[tex]2^0[/tex]=1
Now, we add these all up to find the total grains of rice!
512+256+64+32+16+8+4+2+1=895
Therefore, George has placed a total of 895 grains of rice on the chess board.
I hope that this helps! Have a wonderful day!
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
On the first square, George placed 1 grain of rice.
On the second square, he placed 2 grains.
On the third square, he placed 4 grains.
On the fourth square, he placed 8 grains.
In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.
So,
On the first 10 squares,
1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]
This is a geometric series with a first term of 1 and a common ratio of 2.
The sum of the first n terms of a geometric series.
[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Substituting the values,
[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)
= 1(1 - 1024) / (-1)
= 1023
Therefore,
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
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¿1 y media taza x 9?
Answer: [tex]1\frac{1}{2} *9=\frac{3}{2}*9=\frac{27}{2}=13\frac{1}{2}[/tex]
Step-by-step explanation:
Answer: 27
-------
2
Step-by-step explanation:
Convert 2.5 tons into pounds.
2.5 T =
lb
()) 500 lb
(1) 2,500 lb
1) 5,000 lb
>> 50 lb
Answer:5000 Ib
Step-by-step explanation:
1 tons=2000 pounds
2.5 tons=2.5 x 2000
2.5 tons=5000 pounds or 5000 Ib
2.5 tons is equal to 5,000 pounds.
To convert tons into pounds, you need to know the conversion factor between the two units.
The conversion factor of 2,000 pounds per ton is derived from the definition of a ton.
The ton is a unit of mass commonly used in the United States and is equal to 2,000 pounds.
This value is based on the historical practice of using a ton as a measure of weight for commodities such as coal, ore, and grain.
Over time, it has become a standardized conversion factor in many industries and countries.
1 ton is equal to 2,000 pounds.
So, to convert 2.5 tons into pounds, you would multiply 2.5 by 2,000.
2.5 tons x 2,000 pounds/ton = 5,000 pounds
Therefore, 2.5 tons is equal to 5,000 pounds.
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2x + 3y = 12
Complete the missing value in the solution to the equation.
,8)
Lacy enjoys running around the lake, and Paul enjoys running around the park. Lacy contends that she runs
farther around the lake than Paul runs around the park, and Paul contends the opposite.
To settle their debate, they find satellite images of the lake and the park and juxtapose them on a single
coordinate grid (shown below).
The perimeter of the lake is m
Round the final answer to the nearest meter. Do not round intermediate calculations.
The perimeter of the park is m
Round the final answer to the nearest meter. Do not round intermediate calculations.
Who should win the debate?
Answer:
The perimeter of the lake is 314m. The perimeter of the park is 339 m. Paul should win the debate.
Step-by-step explanation:
Two datasets arranged in descending order are; {8,x , 4,1} and {9,y , 5,2}. If the medians of the two given datasets are equal, what is the value of ( y-x)^2?
Answer:
1Step-by-step explanation:
Median of a dataset is the value at the centre of the dataset after rearrangement.
Given the data {8,x , 4,1}, the median of the set will be two values(x and 4). Since we have two values as the median, we will take their average.
Median of the first data set = x+4/2 ...(1)
For the second dataset {9,y , 5,2}, the median will be y+5/2
Since we are told that the medians of both datasets are equal, we will equate the value of the medians of both datasets as given below;
x+4/2 = y+5/2
cross multiplying;
2(x+4) = 2(y+5)
Dividing both sides by 2 will give;
x+4 = y+5
From the resulting equation;
y-x = 4-5
y-x = -1
(y-x)² = (-1)² = 1
PLEASE HELP!!!
Find the volume of each cylinder. Which cylinder has the greater volume? Use 3.14 for π and round your answers to the nearest hundredth.
Answer:
Cylinder A has a volume of 35.34 and Cylinder B has a volume of 58.9, the cylinder B has the greater volume.
Step-by-step explanation:
B= (3.14) 2.5 x 3h = 58.9 Cylinder B = 58.9
A= (3.14) 1.5 x 5h = 35.34 Cylinder A = 35.34
An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. On the first day of class, she counts 105 students enrolled, of which 19 are repeating the class. The university enrolls 15,000 students.
1. An estimate of the population proportion repeating the class is given by:
a) 0.0013.
b) 0.007.
c) 0.181.
d)0.046.
2. The instructor wishes to estimate the proportion of students across campus who repeat a course during summer sessions and decides to do so on the basis of this class. Would you advise the instructor against it and why:
a) No, because 105 students is a pretty large class.
b) Yes, because this class is too small.
c) No, because it is completely arbitrary who takes this class.
d) Yes, because this class is not a random sample of students.
3. The standard error for the estimated sample proportion is given by:
a) 0.025.
b) 0.0014.
c) 0.0376.
d) 0.005.
4. A 95% confidence interval is given by:
a) 0.15, 0.23.
b) 0.345, 0.453.
c) 0.107, 0.255.
d) 0.09, 0.272.
5. She hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are:
a) H0:p? =0.181 vs. H?:p=0.1 .
b) H0:p=0.1 vs. H?:p?0.18 .
c) H0:p=0.1 vs. H?:p? =0.181 .
d) H0:p=0.1 vs. H?:p?0.1 .
6. The test statistic for this hypothesis is given by:
a) 2.575.
b) 2.332.
c) 2.765.
d) 1.96.
7. The P?value for this test is:
a) 0.05>P>0.01 .
b) P>0.05 .
c) 0.01>P>0.005 .
d) 0.005>P .
8. Based on the p-value found:
a) we have convincing proof that the proportion of students repeating a class during summer sessions is not 10%.
b) we have strong evidence that the proportion of students repeating a class during summer sessions is not 10%.
c) we have strong evidence that the proportion of students repeating a class during summer sessions is 10%.
d) we have no doubt that the proportion of students repeating a class during summer sessions is not 10%.
Answer:
Check the explanations
Step-by-step explanation:
According to given information, an instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. On the first day of class, she counts 105 students enrolled, of which 19 are repeating the class. The university enrolls 15,000 students.
Therefore the number of observation n 105 and enrolled x=19
1. An estimate of the population proportion repeating the class is given by:
c) 0.181.
Explanation:
19 --0.18090,181 n 105
2. The instructor wishes to estimate the proportion of students across campus who repeat a course during summer sessions and decides to do so on the basis of this class. Would you advise the instructor against it and why:
d) Yes, because this class is not a random sample of students.
3. The standard error for the estimated sample proportion is given by:
c) 0.0376.
Explanation:
SE [tex](\hat{p})=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
0.181 × (1-0.181) 105
0,0376 0.0376
4. A 95% confidence interval is given by:
c) 0.107, 0.255.
Explanation:
In order to determine the 95% confidence interval we follow the following step:
Where the z value is determined from the standard normal table as ~ 1.96
[tex]\hat{p}\pm \left [z\times SE(\hat{p}) \right ][/tex]
0.181 ± (1.96 × 0.0376)
0.181 ± 0.0737
Therefore the lower confidence interval is
LCI= 0.181- 0.0737
LCI= 0.107
Therefore the upper confidence interval is
UCI = 0.181 + 0.0737
UCI0.255
Therefore 95% confidence interval is
[tex]\left (0.107,0.255 \right )[/tex]
5. She hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are:
d)[tex]0 :P = 0.10 and H_{a}:p\neq 0.10[/tex]
Explanation:
She hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are defined on the basis of observation,
Null hypothesis as:
[tex]H_{0}[/tex]:p= 0.10
and alternative hypothesis as:
[tex]H_{a}:p\neq 0.10[/tex]
6. The test statistic for this hypothesis is given by:
c) 2.765.
Explanation:
In order to determine the z test statistics as:
Z=[tex]\frac{\hat{p}-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}[/tex]
0.181 - 0.10 0.10x (1-0.10)
=2.765
7. The P value for this test is:
c) 0.01>P>0.005 .
Explanation:
P value is calculated as:
P(Z > 2.765) 0.002845 for one tail test and
P(Z > 2.765) 0.005692 for two tail test.
8. Based on the p-value found:
b) we have strong evidence that the proportion of students repeating a class during summer sessions is not 10%.
Explanation:
As the z observed is more than the tabulated z value at 95% as:
[tex]Z_{observed}=2.765> Z_{tabulated}=1.96[/tex]
and also P value is less than the [tex]\alpha =1-0.95=0.05[/tex]
[tex]P(Z\geq 2.765)=0.005692< \alpha =0.05[/tex]
Therefore we accept the alternative hypothesis and we may conclude that we have strong evidence that the proportion of students repeating a class during summer sessions is not 10%.
Solve the proportion.
3x / 10 = 9 / 4
Answer:
x =7.5
Step-by-step explanation:
We can use cross products to solve
3x / 10 = 9 / 4
3x*4 = 10*9
12x = 90
Divide each side by 12
12x/12 = 90/12
x =7.5
Harper went to the candy store and bought 3/8 of a pound of candy. If 1/2 of Harper's candy
was chocolate, how many pounds of chocolate candy did Harper buy?
Write your answer as a fraction or as a whole or mixed number.
Answer:
The answer is 3/16 pounds of chocolate
Answer:3/16
Step-by-step explanation:
a pound of candy is 1
Harper bought 3/8 of 1
3/8 x 1=3/8
1/2 of harper candy = chocolate
1/2 of 3/8
1/2 x 3/8=3/16
BRAINLIEST ASAP! LENGTH OF AC?
Answer:
2.33 units
Step-by-step explanation:
[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]
S. Solve the following system of equations algebraically.
3x-y = 0
5x + 2y = 22
Part II: Combine the two equations to eliminate one of the variables. Show the result of this
combination below. (2 points)
Answer:
11x = 22(x, y) = (2, 6)Step-by-step explanation:
Twice the first equation can be added to the second to eliminate the variable y.
2(3x -y) +(5x +2y) = 2(0) +(22)
11x = 22 . . . . . . . the result of the combination
__
Solving this gives ...
x = 2
Substituting into the first equation gives ...
3(2) -y = 0
y = 6
The solution is (x, y) = (2, 6).
Solve the inequality
Math question
Answer:
AAAAAAAAAAAAAAAAAAAA
Step-by-step explanation:
x < 7
Every hour the number of users of a new smartphone app increases by 18 percent. At 1:00 p.m., there were 12,322 users. What exponential equation shows the number of users' x hours after 1:00 p.m.?
Answer:
B
Step-by-step explanation:
Y is the starting point so it would be y=12322 and it becomes 1.18 because you add 100 to 18
The exponential equation shows the number of users x hours after 1:00 p.m will be y = 12322 (1.18)ˣ. Option A is correct.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The number of users of a new smartphone app increases by % = 18
a is the number of users at 1:00 p.m = 12,322
The exponential equation shows the number of users x hours after 1:00 p.m. is;
y=a(z)ˣ
Where,
a is the initial value
z is the percentage increment
y is the number of users after the given period
If the initial value of the percentage is 100.The value after the given time;
z = 100 + 18
z = 118
The z in the percentage form is 1.18.
The exponential equation shows the number of users x hours after 1:00 p.m will be y = 12322 (1.18)ˣ.
Hence, option A is correct.
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If the first term of an arithmetic sequence is 4 and the difference between con-
secutive terms is 5, what is the second term? The third term? The twelfth? The
eightieth? The nth?
Answer:third term=14 twelfth term=59
Step-by-step explanation:
first term=a=4
Common difference=d=5
Second term=4+5=9
Third term=9+5=14
Using Tn=a+d(n-1)
T12=4+5(12-1)
T12=4+5x11
T12=4+55
T12=59
Twelveth term=59
Will get the brainiest answer for this problem involving a number line!
Answer:
61/1513/15Step-by-step explanation:
The fill-in for the first box is found by counting spaces between 0 and 2/5. There are 6 of them.
__
Since 6 spaces = 2/5, the value of 1 space is 1/6 of 2/5. We must multiply 2/5 by 1/6 to find the value of 1 space:
1 space = (2/5)(1/6) = 2/30 = 1/15
This is the number that goes in the second box.
__
To find the value of x, count all the spaces. There are 13, so the value of x is 13 times the value of 1 space:
x = 13(1/15) = 13/15
This is the number that goes in the last box.
(2u + 7)(3u – 1) = 0 solve buy factoring
Answer:
Factor and set each factor equal to zero.
u = - 7 /2,1/3
WHO EVER HELP MES WILL GET BRAINLEST. AND ALL MY POINTS PLZ HELP ME FIND THE AREA OF THIS
Answer:
5 in^2
Step-by-step explanation:
2x2 for the square = 4 in
1x2/2 for the triangle = 1 in
Answer:
so find the area of the swuare first. 2 times 2 = 4. then you have to add that to the area of the triangle which is 1/2 times base times height. We know that the height is 1 and the base is 2 (from the square's common side shared) so its gonna be 2 times 1 which is 2 divided by 2 which is one soo its 4+1=5
so the answer is 5 inches squared
Step-by-step explanation:
A soccer ball is inflated so that it’s diameter is 12 inches.about how much air does it hold?
Answer:
About [tex]905in^{3} of air[/tex]
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes. a sphere
yes an inflate ball takes the shape of a sphere.
Given data
Volume v = ?
Diameter d= [tex]12 in[/tex]
Radius r = [tex]\frac{diameter}{2} = \frac{12}{2} = 6in[/tex]
The expression for the volume of a sphere is
[tex]volume= \frac{4}{3}\pi r^{3} \\volume= \frac{4}{3} *3.142*6^{3} \\volume= \frac{12.57}{3} *216\\volume= \frac{2715.12}{3}\\ volume = 905.04 in^{3}[/tex]
Approximately the ball hold about [tex]905in^{3} of air[/tex]
The area of a circle is 286 cm2. Use the π button on your calculator for π in your calculations.
8a
If its radius is r cm, find r, correct to 2 decimal places.
Be careful not to round your answer until the very end.
Answer:
9.54 cm
Explanation:
area = πr^2
286 cm^2= πr^2
=>πr^2= 286 cm^2
=>r^2= 286÷π
=>r= √286÷π
: 9.54. m
circumference=2πr
=> circumference=2×π×9.54
=60 cm
HELP PLEASE, 10 points
The diameter of the hemisphere is 16 inches. What is the total surface area of the hemisphere?
Round to the nearest whole number.
Answer:
Step-by-step explanation:
d = 16 cm
r =16/2= 8 cm
Total surface area = 3πr² cubic units
= 3 * 3.14 * 8 * 8
= 602.88
= 603 cm²
If a coin is flipped three times, how many possible outcomes will include exactly 2 tails?
Answer:
If a coin is flipped three times, possible outcomes would be:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
=> possible outcomes that will include exactly 2 tails:
HTT
THT
TTH
TTT
Hope this helps!
:)
Answer:
The answer is 3 or option B.
Step-by-step explanation:
I just answered the question.
Tessa and her friends decided to have a water balloon fight! They got 20 water balloons and used 6 liters of water to fill them all equally. How much water was in each balloon?
Answer:
The amount of water is each balloon should be:
A = 6/20 =0.3 liters
Hope this helps!
:)
Answer:
0.3
Step-by-step explanation:
.
3. Jada is making a scale model of the solar system. The distance from Earth to the
moon is about 2.389 x 10 miles. The distance from Earth to the sun is about
9.296 X 10' miles. She decides to put Earth on one corner of her dresser and the
moon on another corner, about a foot away. Where should she put the sun?
o On a windowsill in the same room?
o In her kitchen, which is down the hallway?
o A city block away?
Explain your reasoning.
Answer:
kitchen
Step-by-step explanation:
if a foot is 2.389 then i would be pretty far but not a block away
What’s the correct answer for this?
Answer:
C
Step-by-step explanation:
HJN IS SIMILAR TO PQN
What Is the product of the polynomials below? (7x^2+2x+4)(2x+5)
Answer:
14x^3+39x^2+18x+20
Step-by-step explanation:
Answer:14x^3+39x^2+18x+20
Step-by-step explanation:
(7x^2+2x+4)(2x+5)
14x^3+35x^2+4x^2+10x+8x+20
Add like terms
14x^3+39x^2+18x+20
What is the volume of a cylinder with a base radius of 4 and height 7?
Answer:
351.86
Step-by-step explanation:
Which method would determine the volume of the prism with dimensions 2x2x4 shown below?
2 in
4
There are 8 one-quarter cubes and 16 unit cubes so 8x
00
+16 will give the volume
A company rents water tanks shaped like cylinders. Each tank has a diameter of 6 feet and a height of 2 feet. The cost is $4 per cubic foot. How much does it cost to rent one water tank?
Answer:
226.08
Step-by-step explanation:
im pretty sure
