Find the sum of the first 9 terms in the following geometric series.
64 + 32 + 16 + ...
Answer: 64 + 32 + 16 + 8 + 4 + 2 + 1 + .5 + .25 = 127.75
Step-by-step explanation: the sequence divides the next number by 2 ; 64/2 = 32, 32/2 = 16, etc
Answer:
127.75
Step-by-step explanation:
A French class has a total of 26 students. The number of males is 10 more than the number of females. How many males and how many females are in the class?
Answer:
10 Male
16 Female
Step-by-step explanation:
There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Write a system of equations that represents the situation and find out how many animals were horses and how many were chickens?
Final answer:
there were 7 horses and 8 chickens in the barn.
Explanation:
To represent the situation with a system of equations, let's assume that the number of horses is represented by 'h' and the number of chickens is represented by 'c'.
We know that there are a total of 15 animals, so we can write the equation: h + c = 15.
We also know that the total number of legs is 44, and since each horse has 4 legs and each chicken has 2 legs, we can write the equation: 4h + 2c = 44.
To solve this system of equations, we can use the method of substitution or elimination. Substituting h = 15 - c into the second equation, we get 4(15 - c) + 2c = 44. Simplify and solve for c to find the number of chickens, then substitute the value of c back into the first equation to find the number of horses.
Let's solve this system of equations:
h + c = 15
4h + 2c = 44
We can solve this using the method of substitution:
h = 15 - c
Substituting this into the second equation:
4(15 - c) + 2c = 44
60 - 4c + 2c = 44
-2c = 44 - 60
-2c = -16
c = -16/-2
c = 8
Substituting the value of c back into the first equation:
h + 8 = 15
h = 15 - 8
h = 7
So, there were 7 horses and 8 chickens in the barn.
Find two numbers, if their sum is 93 and their difference is 9.
Answer:
51 and 42
Step-by-step explanation:
Use
x + y = 93
x - y = 9
Add those two equations together and you get 2x = 102
*y is not in the equation anymore because y + -y = 0*
Divide both sides by 2
x = 51
plug x into one of the equations; let's use x + y = 93
Then you get, 51 + y = 93
Subtract both sides by 51 and you get y = 42
Plug both in the other equation to make sure the numbers work.
51 + 42 = 93; true
51 - 42 = 9; true
Answer:
42 and 52
Step-by-step explanation:
Which is the angle measure represented by 7.5 rotations clockwise?
a. -2700°
c. 2700
b. -1350°
d. 1350°
Answer:
The angle measure is 2700°
Step-by-step explanation:
Close wise rotation is positive.
Note that one rotation is equivalent to a revolution.
If one rotation = 360°
7.5 rotations will measure 360° ×7.5 which is equivalent to 2700°
ILL GIVE YOU BRAINLIEST!! Pat needs 19 balloons for a water balloon fight. About how many ounces of water will he need if each balloon holds 2 ounces of water?A. 40 ounces B. 19 ounces C. 30 ounces D.50 ounces E. 20 ounces
Answer:
A
Step-by-step explanation:
If each balloon holds 2 oz of water, you can multiply 19 by 2 to find out how many ounces you'll need. 19*2 is equal to 38, but rounding up is 40.
The total amount of water needed by Pat for the balloon fight is 40 ounces.
The correct option is (A).
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers and their relationships.
As per the given data:
The number of balloons needed for a fight is equal to 19.
The amount of water each water balloon holds is also given.
We have to find out the total amount of water needed by Pat for the balloon fight.
The amount of water each water balloon holds = 2 ounces
Total amount of water needed by Pat for the balloon fight:
= number of balloons needed for a fight × amount of water each water balloon holds
= 19 × 2
= 38 ounces (after rounding off to the tenths place, it's equal to 40)
= 40 ounces
Hence, the total amount of water needed by Pat for the balloon fight is 40 ounces.
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A rectangular prism has a volume of 1,200 cubic units. The prism has a length of 24 units and a height of 5 units. What is the width of the prism?
Answer:
10 units
Step-by-step explanation:
Divide the volume by the product of the length and height to calculate the rectangular prism's width.
1200 / 24 x 5 = 10 units
Solve for x in the following:
X^2 + 10x + 29=0
Answer:
x= [tex]-5+2i, -5-2i[/tex] aka No Real Solution
How many ways can you write y^6 as the product of two powers?
Answer:
4
Step-by-step explanation:
Write y6 as a product of two powers with the same base in four different ways, using negative or zero exponents in each product.
What are the solutions to x2 - 6x - 7 = 0?
Answer:
x=7 x=-1
Step-by-step explanation:
x^2 - 6x - 7 = 0
Factor
What two numbers multiply to -7 and add to -6
-7*1 =-7
-7+1 = -6
(x-7) (x+1) = 0
Using the zero product property
x-7 =0 x+1 =0
x=7 x=-1
Answer: x is -1 & 7
Step-by-step explanation:
X2-6x-7=0
Quadratic equation
Variables of -7 that will give-6 are
-7 & +1
X2-7x+x-7=0
X(x-7) +1(x-7)=0
(X+1)(x-7)=0
X+1=0
X= -1 or
X-7=0
X= 7
Therefore,
X is either -1 & 7
What is 27% of 76,200
You can evaluate every percentage in two simple steps:
First of all, divide your number by 100. This will give you the 1% of your quantity:
[tex]\dfrac{76200}{100}=762[/tex]
Then, multiply the 1% by 27 to get the 27%:
[tex]762\cdot 27=20574[/tex]
27% of 76,200 is 20,574.
"To calculate 27% of 76,200, one can multiply the total amount by the percentage value, expressed as a decimal or fraction. Here is the step-by-step calculation:
First, convert the percentage to a decimal by dividing by 100:
"To calculate 27% of 76,200, one can multiply the total amount by the percentage value, expressed as a decimal or fraction. Here is the step-by-step calculation:
First, convert the percentage to a decimal by dividing by 100:
[tex]\[ 27\% = \frac{27}{100} = 0.27 \][/tex]
Next, multiply this decimal by the total amount:
[tex]\[ 0.27 \times 76,200 = 20,574 \][/tex]
Therefore, 27% of 76,200 is 20,574.
The answer is: 20,574."
A chef at a restaurant uses 14 pounds of butter each day. About how many grams of butter does the chef use each day Start Fraction 16 ounces Over 1 pound End Fraction
and Start Fraction 28.4 grams Over 1 ounce End Fraction
Answer:
6361.6 grams
Step-by-step explanation:
A chef at a restaurant uses 14 pounds of butter each day
Given;
16 ounces per pound
And
28.4 grams per ounces
Converting 14 pounds to gram;
14 pounds × 16 ounces/pound = 224 ounces
Then;
224 ounces × 28.4 grams/ounce = 6361.6 grams
What is the area of this figure?
Answer:
1240 yd²
Step-by-step explanation:
Answer: 1440 square units
Step-by-step explanation:
40 x 36
A = L x w
Which inequality best represents the following situation: The speed limit in your neighborhood is 30 miles an hour and you are not breaking the law.
Answer:
D
Step-by-step explanation:
You can drive anywhere less than or equal to 30 mph, and it'd be legal
A circle with the are 16pi has a sector with the central angel of 8/5 radians
Answer:
3/2 units^2
Step-by-step explanation:
The area of the entire circle is 16π. What is the area of a sector of this circle if the central angle (not angel) is 8/5 radians?
Formula: (fraction of circle represented by the sector)(area of the circle
Area of the sector described above is
8/5 radians 8*16π square units
----------------------- * 16π square units = ------------------------------ = 3/2 units^2
2π radians 10π
Simplify each expression 8+7y-3y+2-4
A bar graph is shown. The x-axis is labeled 1 through 9 and the y-axis is labeled 0, 5, 10, 15. Bar 1 is 2 units high, bar 2 is 4 units high, bar 3 is 6 units high, bar 4 is 8 units high, bar 5 is 10 units high, bar 6 is 8 units high, bar 7 is 6 units high, bar 8 is 4 units high, and bar 9 is 2 units high.
Which of the following statements is true about a graph that is perfectly symmetric, such as the one above?
The mean is greater than the median.
The mean is equal to the median.
The mean is less than the median.
Answer:
the mean is equal to the median
Step-by-step explanation:
From the bar graph,
The mean is equal to the median.
Option B is the correct answer.
What is a bar graph?A bar graph is a type of chart used to represent data using rectangular bars, where the length or height of each bar corresponds to the value of the data.
The bars can be arranged horizontally or vertically and are usually separated by equal spaces.
The x-axis represents the categories or groups being compared, and the y-axis represents the scale or measurement of the data being shown.
We have,
For a graph that is perfectly symmetric, the mean and median are equal.
In the given bar graph, the bars are perfectly symmetric around the middle bar, which is bar 5.
This means that the median value of the data represented by the graph is 5.
To find the mean of the data, we can add up the heights of all the bars and divide by the total number of bars:
(2 + 4 + 6 + 8 + 10 + 8 + 6 + 4 + 2) ÷ 9 = 6
So the mean value of the data is also 6.
Therefore,
The mean is equal to the median.
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For a standard normal distribution, which of the following variables always equals 1?
Mu
Sigma
x
z
Answer:
The mean is 0 and the deviation 1. And we can express this distribution with the following notation:
[tex] Z \sim N (\mu =0,\sigma =1)[/tex]
[tex]\sigma = 1[/tex] correct the deviation for this special distributionn is always 1
Step-by-step explanation:
The normal standard distribution is an special case of the normal distribution with some parameters on specific.
The mean is 0 and the deviation 1. And we can express this distribution with the following notation:
[tex] Z \sim N (\mu =0,\sigma =1)[/tex]
And when we analyze the options we can conclude this:
[tex]\mu[/tex] this value for this distribution is always equal to 0 and not 1
[tex]\sigma = 1[/tex] correct the deviation for this special distributionn is always 1
[tex]x[/tex] this value can be any value higher or lower than 1 so then is not the correct option
[tex]z[/tex] this variable can be different from 1 so then is not the correct option
Answer:
The mean is 0 and the deviation 1. And we can express this distribution with the following notation:
correct the deviation for this special distributionn is always 1
Step-by-step explanation:
The normal standard distribution is an special case of the normal distribution with some parameters on specific.
The mean is 0 and the deviation 1. And we can express this distribution with the following notation:
And when we analyze the options we can conclude this:
this value for this distribution is always equal to 0 and not 1
correct the deviation for this special distributionn is always 1
this value can be any value higher or lower than 1 so then is not the correct option
this variable can be different from 1 so then is not the correct option
Step-by-step explanation:
Most married couples have two or three personality preferences in common. Myers-
Briggs used a random sample of 375 married couples and found that 132 had three
preferences in common. Another random sample of 571 couples showed that 217 had
two personality preferences in common. Find a 90% confidence interval for the
proportion of married couples with three personality preferences in common compared
with the proportion of couples with two preferences in common. (Show your confidence
in interval notation and show your interpretation, which was larger?
Answer:
The 90% confidence interval for the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common is (-0.081, 0.025).
Step-by-step explanation:
The (1 - α)% confidence interval for difference in proportion formula is,
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
The given information is:
n₁ = 375,
n₂ = 571,
X₁ = 132,
X₂ = 217.
Compute the sample proportion as follows:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{132}{375}=0.352\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{217}{571}=0.38\\[/tex]
For the 90% confidence level, the z-value is,
z₀.₀₅ = 1.645
*Use a z-table.
Compute the 90% confidence interval for the difference in proportion as follows:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
[tex]=(0.352-0.38)\pm 1.645\sqrt{\frac{0.352(1-0.352)}{375}+\frac{0.38(1-0.38)}{571}}\\=-0.028\pm 0.05256\\=(-0.08056, 0.02456)\\\approx (-0.081, 0.025)[/tex]
The 90% confidence interval for the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common is (-0.081, 0.025).
This confidence interval implies that the true difference between the proportions lies in this interval with probability 0.90.
The 90% confidence interval for the difference in proportions of married couples with two and three personality preferences in common is (0.027, 0.089). This indicates that with 90% confidence, the proportion of couples with two preferences in common is significantly higher.
Explanation:Firstly, we need to find the proportions for both samples. The proportion for three personality preferences in common is 132/375 = 0.352 and for two personality preferences in common is 217/571 = 0.380.
Next, to compute the standard error, we use the formula √[ P(1 - P) / n ]. For three personality preferences we get √[ 0.352(1 - 0.352) / 375] = 0.026. And for two personality preferences we obtain √[ 0.380(1 - 0.380) / 571] = 0.021.
From these, the difference in the two sample proportions can be calculated, which is 0.380 - 0.352 = 0.028. The standard error of the difference can then be calculated as √( 0.026 ^ 2 + 0.021 ^ 2) = 0.033. At the 90% confidence level, the z-score is 1.645.
To calculate the confidence interval, note that 0.028 ± 1.645 * 0.033 is the equation we are trying to solve. This produces a range from 0.027 to 0.089.
So, the 90% confidence interval for difference in proportions is (0.027, 0.089), meaning that with 90% confidence, the proportion of couples with two preferences in common is significantly higher than those couples with three personality preferences in common.
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The unit of measure of the of the conversion factor should be the unit of
measure which you want to convert.
The correct use of conversion factors will result in the cancellation of the unwanted units and retention of the desired unit.
Conversion factors are essential in unit conversions, allowing us to switch from one unit of measurement to another within the same system, such as U.S. customary units or the SI unit system. To use conversion factors effectively, one must ensure that the unit of measure they wish to convert from or to is correctly positioned in the conversion factor equation. For instance, when converting meters to centimeters, a factor of 1 cm/10-2 m or 100 cm/1 m is used because 'centi' means 10-2 in the SI unit system.
It is important to keep track of units being canceled during the conversion. If you have units in the numerator and denominator that are the same, they will cancel out, leaving only the desired unit. In the process of conversion, if the unit you want to convert is in the denominator of the original quantity, the conversion factor should have that unit in the numerator.
Choosing the right conversion factor and accurately performing the calculations are crucial. A proper conversion factor will cancel out unwanted units. Using an incorrect conversion factor without an opposing unit to cancel out will leave an unwanted unit in your answer, indicating an error in the process.
Dimensional analysis, which often involves conversion factors, simplifies the process of converting units and ensures that measurements within calculations are consistent. This technique is fundamental for scientific calculations and everyday applications, such as determining the appropriate unit to measure large volumes or distances.
Which polynomials are in standard form?
Choose all answers that apply:
5 – 20
® 24 – 8x2 – 16
©
523 + 4x4 – 32 +1
0
None of the above
Answer:
None of the above
Step-by-step explanation:
None of the above polynomials are in standard form.
Race Times
29 min.
31 min.
31 min.
34 min.
35 min.
37 min.
40 min.
42 min.
45 min.
Sarabeth used a box-and-whisker plot to summarize her race times in minutes. She didn't include her latest race time of 38 minutes. How will the inclusion of this new time affect the box-and-whisker plot?
A) The range will increase.
B) The median will increase.
C) The lower quartile will increase.
D) The upper quartile will increase.
Answer:
B) The median will increase.
Step-by-step explanation:
he original median was 35 and the new median is 36. The median will increase.
is 4/x^4+3/x^3-2/x^2-1 a polynomial
Given f(x) = -10x + 45, find x when f(x) = 15.
Answer:
3 =x
Step-by-step explanation:
f(x) = -10x + 45
f(x) = 15
15 = -10x +45
Subtract 45 from each side
15-45 = -10x+45-45
-30 = -10x
Divide each side by -10
-30/-10 = -10x/-10
3 =x
What is the volume of this square pyramid?
and can someone answer my last question
Answer:
The answer is 600
Step-by-step explanation:
V = A(h/3)
The sum of two consecutive even numbers is 206. What is the value of the smallest number?
Answer:
102
Step-by-step explanation:
Since we know that the numbers are two consecutive even numbers, we can write an equation like this where n represents the 2 numbers.
n + (n+2) = 206
Simplify the left side:
n + (n+2) = 206 -----> 2n+2 = 206
Subtract 2 from both sides:
2n = 206-2 -----> 2n = 204
Now divide 204 by 2:
n = 204/2 -----> n = 102
The smallest of two consecutive even numbers, whose sum is 206, is 102.
Explanation:The question is asking for the smallest of two consecutive even numbers whose sum is 206. Let’s denote the smaller even number by n. The next consecutive even number would be n+2 (since even numbers are two units apart).
The problem states that the sum of these two numbers is 206 which can be written in the equation form as n + (n+2) = 206. It simplifies to 2n + 2 = 206. Subtracting 2 from both sides, we get 2n = 204. And finally, dividing by 2, we find that n = 102. So, the smallest number is 102.
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A class of 24 students is having a drawing. Each student's name is placed on a piece of paper and then placed in a hat. One name is randomly drawn from the hat.
If there are 12 boys in the class, what is the probability that the name drawn is a girl's?
A. 1/2
B. 11/24
C. 11/12
D. 13/24
The probability of drawing a girl's name from a hat with 24 students of which 12 are boys is 1/2 or 50%.
The question is regarding the probability that a randomly drawn name is a girl's if there are 24 students in a class with 12 boys. Since the number of girls must be 24 total students minus 12 boys, which leaves us with 12 girls, the probability of drawing a girl's name is the number of girls over the total number of students. Therefore, the probability is 12 girls divided by 24 students, which simplifies to 1/2.
1/2(b+14)=b+14/2. What is the solution to this
The equation 1/2(b + 14) = b + 14/2 simplifies to 14 = 14, suggesting that any value for b is a solution, and the equation is an identity.
The given equation is 1/2(b + 14) = b + 14/2. To solve for the variable b, we can perform algebraic operations. First, we recognize that the equation on the left side is already simplified, but we need to clarify whether the denominator 2 applies to the whole right-hand side or just to the 14 in the equation b + 14/2. Assuming it applies only to the 14, we can multiply both sides of the equation by 2 to eliminate the denominators:
1/2(b + 14) * 2 = (b + 14/2) * 2b + 14 = 2b + 14After simplifying, we see that b on both sides cancels out, leaving us with an equality 14 = 14, which is always true. This means that the equation has infinitely many solutions, since any value of b will satisfy the equation. If the denominator 2 applied to the entire right-hand side (b + 14), then the equation is already balanced as written, again indicating that any value of b would be a solution.
This balance shows that the original equation represents an identity rather than a conditional equation with a specific solution.
A delivery company has 18 vehicles in its fleet. it has 8 vans and 10 trucks All 18 vehicles are on the road every working day The company is reviewing its fuel expenses and therefore gathers some information about each type of vehicle VAN=> average distance travelled per day (in km) is 198 and its average distance travelled per litre is 9 TRUCK=>average distance travelled per day (in km) is 620 and its average distance travelled per litre is 6.2 All the vehicles use the same type of fuel at £1.29 per litre Use this information to work out the bill for 1 working day. You must show all of your working
Answer:
$157.38 per day is used.
Step-by-step explanation:
Van distance 198
9km per L
198÷9=22L
Truck distance 620
6.2km per L
620÷6.2=100L
truck 100L
+van 22L
=122Lx1.29
=157.38
Daily fuel consumption is calculated for trucks and vans by dividing their respective average distances travelled per day by their averages distances travelled per litre. These amounts are multiplied by the respective numbers of each vehicle and then by the cost of fuel (£1.29 per litre) to give a total daily fuel bill of £1,517.04.
Explanation:The first step in calculating the daily bill for the delivery company is to determine how many litres of fuel both the vans and trucks consume per day. To do this, divide the average distance travelled per day by the average distance travelled per litre for each type of vehicle.
For the vans, this would be 198 / 9 = 22 litres per day. For the trucks, 620 / 6.2 = 100 litres per day.
The company has 8 vans and 10 trucks, so the total daily fuel consumption would be: (8 * 22) + (10 * 100) = 176 + 1000 = 1176 litres.
The cost of fuel is £1.29 per litre, so the daily bill would be 1176 * £1.29 = £1,517.04.
Therefore, the delivery company's total fuel bill for one working day is £1,517.04.
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What are the coordinates of vertex A of square ABCD?
Square A"B"C"D" is the final image after the rule
T-A-R .(X.) was applied to square ABCD.
(-1,-6)
(-1.-2
(-1,6)
(-2.1)
Answer:
(-2, 1)
Step-by-step explanation:
The coordinates of the vertex A of square ABCD is (1, 6).
What is Translation?Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.
Given that,
A square ABCD undergoes a translation of (-4, -1) and a rotation of 90° to form the square A''B''C''D''.
Let (x, y) be the coordinates of A.
After the translation of (-4, -1), it becomes,
A'(x - 4, y - 1)
When it rotates to 90°, it becomes,
A''(-(y - 1), x - 4) = A''(1 - y, x - 4) = (-5, -3)
1 - y = -5 ⇒ y = 1 + 5 = 6
x - 4 = -3 ⇒ x = 1
Coordinates are (1, 6)
Hence the coordinates of A is (1, 6).
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The complete question is as follows :
Square A"B"C"D" is the final image after the rule T -4, -1 • R 0, 90° (x, y) was applied to square ABCD. What are the coordinates of vertex A of square ABCD?
n a coordinate plane, a square A double-prime B double-prime C double-prime D double-prime has points (negative 5, negative 3), (negative 3, negative 1), (negative 1, negative 3), (negative 3, negative 5).