Answer:
27 and 60
Step-by-step explanation:
lets say the first number 'a' and the second number 'b'
1) The question says the sum of two number is 87 which means a + b = 87........given 1
2) we have another given which says one of the number is 6 morethan twice the other which means a = 2b + 6.......... given 2
a + b = 87
2b + 6 + b = 87 (we substitute 'a' with the given 2b + 6)
3b + 6 = 87
3b = 87 - 6
3b = 81
3b = 81
3 3
b = 27 ..... the first number
a = 2b + 6
a = 2 × 27 + 6
a = 54 + 6
a = 60..... the second number
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For any question comment me
how much time with it take for 450 to yield 81 as interest at 4.5 per annum of simple interesst
Answer:
4 years
Step-by-step explanation:
The formula for simple interest is useful here.
I = Prt
where P is the principal invested at rate r for t years.
Fill in the given values and solve for t:
81 = 450×0.045×t
81/20.25 = t = 4
It will take 4 years for 450 to yield 81.
Evaluate the expression (7+6i)−(−9−8i) and write the result in the form a+bi.
Remove the parentheses and combine the like terms:
7 - -9 = 7+ 9 = 16
6i - -8i = 6i +8i = 14i
The answer is 16 + 14i
Find the distance between X (5, 7) and Y (-6, 6).
Round answer to the nearest tenth.
Answer: 11.0 or 11
Step-by-step explanation:
To find the distance first find the difference between the coordinates. find the change in the x and y coordinates and square them to add them to get a number and find the square root of that same number to find the distance.
x coordinates: 5-(-6)= 11
y coordinate: 7-6 = -1
Now square them
11^2 + 1^2 = l^2 where l is the distance
121 + 1 = l^2
122 =l^2
l = [tex]\sqrt{122}[/tex]
l = 11.045 Rounded to the nearest tenth is 11.0
A snack bar seils scoops of strawberry, chocolate, and
vanilla ice cream. On Monday, the snack bar sold
100 scoops in total of these flavors of ice.cream. The
snack bar sold 3 times as many scoops of chocolate as
it did strawberry and 2 times as many scoops of
vanilla as it did chocolate. How many scoops of
chocolate ice cream did the 'snack bar sell on
Monday?
Answer:
600/11
Step-by-step explanation:
scoops of
strawberry= x
chocolate= y
vanilla ice cream= z
X+y+z= 100
The snack bar sold 3 times as many scoops of chocolate as it did strawberry
3x= y
X= y/3
and 2 times as many scoops of
vanilla as it did chocolate
2z= y
Z= y/2
X+y+z= 100
Y/3 + y +y/2 = 100
2y + 6y + 3y = 600
11y= 600
Y= 600/11
Which operation would be completed second in the following expression?
33 + 11-10-2x4
simplify the exponent
add
divide
multiply
Answer:
I THINK IT WILL BE HELPFUL
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (XY) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y)
midpoint (5. - 12), endpoint (4-7)
The other endpoint is
(Type an ordered pair)
Answer:
(6, -17)
Step-by-step explanation:
Given the coordinate of a midpoint, (5, -12), and one endpoint, (4, -7), the other endpoint can be determined as follows:
The midpoint formula is given as [tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex].
Since we are given ordered pairs of the midpoint and one endpoint, we would find the other ordered pair of the endpoint as shown below.
Let the other endpoint be [tex] (x_1, y_1) [/tex]
Midpoint = M(5, -12)
Let the given endpoint = [tex] (4, -7) = (x_2, y_2) [/tex]
Thus:
[tex] M(5, -12) = (\frac{x_1 + 4}{2}, \frac{y_1 +(-7)}{2}) [/tex]
Rewrite the equation to find the coordinates of the other endpoints
[tex] 5 = \frac{x_1 + 4}{2} [/tex] and [tex] -12 = \frac{y_1 - 7}{2} [/tex]
Solve for each:
[tex] 5 = \frac{x_1 + 4}{2} [/tex]
[tex] 5*2 = \frac{x_1 + 4}{2}*2 [/tex]
[tex] 10 = x_1 + 4 [/tex]
[tex] 10 - 4 = x_1 + 4 - 4 [/tex]
[tex] 6 = x_1 [/tex]
[tex] x_1 = 6 [/tex]
[tex] -12 = \frac{y_1 - 7}{2} [/tex]
[tex] -12*2 = \frac{y_1 - 7}{2}*2 [/tex]
[tex] -24 = y_1 - 7 [/tex]
[tex] -24 + 7 = y_1 - 7 + 7 [/tex]
[tex] -17 = y_1 [/tex]
[tex] y_1 = -17 [/tex]
Ordered pair of the other endpoint is (6, -17)
Point P is on line segment OQ. Given OP = 14 and OQ = 16, determine the
length PQ
Answer:
PQ = 2
Step-by-step explanation:
We know that OQ = OP + PQ. Since OQ = 16 and OP = 14, we know that 16 = 14 + PQ, therefore, PQ = 2.
Determine ux and sigma x from the given parameters of e population and sample size.
mu = 86, sigma = 16, n = 64
Suppose a simple random sample of size n = 36 is obtained from a population with mu = 71 and sigma = 6.
A) Describe the sampling distribution of xbar.
B) What is P (xbar > 73)?
C) What is P (xbar 69)?
D) What is P (69.8 < xbar < 72.5)?
1) Choose the correct description of the shape of the sampling distribution of xbar.
A) The distribution is skewed left.
B) The distribution is approximately normal.
C) The distribution is uniform.
D) The distribution is skewed right.
E) The shape of the distribution is unknown.
Find the mean and standard deviation of the sampling distribution of x-.
2) P(x->73) =.
3) P (x- 69) =.
4) P (69.8 < xbar < 72.5) =.
Answer:
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 86
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 2
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 71
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 1
B) The distribution is approximately normal.
[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]
Therefore, the probability that the sample mean is greater than 73 = 0.0228
[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]
The probability that the sample mean is less than or equal to 69 is 0.0228
[tex]\mathbf{P( 69.8 \leq \overline x \leq 72.5) = 0.8181}[/tex]
Thus, the probability that the sample mean is between 69.8 and 72 is 0.8181.
Step-by-step explanation:
We are to determine the [tex]\mu_{\overline x}[/tex] and [tex]\sigma_x[/tex] from the given parameters of a population and sample size.
Given that :
population mean [tex]\mu[/tex] = 86
population standard deviation [tex]\sigma[/tex] = 16
sample size n = 64
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is equal to the population mean [tex]\mu[/tex]
∴
[tex]\mu_{\overline x}[/tex] = [tex]\mu[/tex] = 86
The standard deviation of the sampling distribution can be computed by using the formula:
[tex]\sigma_{\overline x } = \dfrac{\sigma }{\sqrt{n}}[/tex]
[tex]\sigma_{\overline x } = \dfrac{16 }{\sqrt{64}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{16 }{8}[/tex]
[tex]\mathbf{\sigma_{\overline x } = 2}[/tex]
∴
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 86
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 2
Suppose a simple random sample of size n = 36 is obtained from a population with mu = 71 and sigma = 6.
i.e
sample size n = 36
population mean [tex]\mu[/tex] = 71
standard deviation [tex]\sigma[/tex] = 6
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is equal to the population mean [tex]\mu[/tex]
∴
[tex]\mu_{\overline x}[/tex] = [tex]\mu[/tex] = 71
The standard deviation of this sampling distribution [tex]\sigma_{\overline x}[/tex] can be estimated as :
[tex]\sigma_{\overline x }= \dfrac{\sigma }{\sqrt{n}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{6 }{\sqrt{36}}[/tex]
[tex]\sigma_{\overline x } = \dfrac{6 }{6}[/tex]
[tex]\mathbf{\sigma_{\overline x } = 1}[/tex]
∴
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 71
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 1
A)
The correct option from the given question is:
B) The distribution is approximately normal.
B) What is P (xbar > 73)?
i.e
[tex]P(\overline x >73) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 \times 6 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{12 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > 2 \end {pmatrix}[/tex]
[tex]P(\overline x >73) = 1- P \begin {pmatrix} Z < 2 \end {pmatrix}[/tex]
Using the Excel Function ( =NORMDIST(2) )
[tex]P(\overline x >73) = 1- 0.9772[/tex]
[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]
Therefore, the probability that the sample mean is greater than 73 = 0.0228
C) What is P (xbar ≤ 69)?
i.e
[tex]P(\overline x \leq 69) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{69 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix}Z \leq \dfrac{-2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-2 \times 6 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-12 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq -2 \end {pmatrix}[/tex]
Using the EXCEL FUNCTION ( = NORMSDIST (-2) )
[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]
The probability that the sample mean is less than or equal to 69 is 0.0228
NOTE: This text editor can't contain more than 5000 characters so the last part of the question is attached in the image below.
If you want to go bed a 800 o'clock
at night and set the alarm to get up at
9 in the morning how many hours
sleep would this permt you?
Answer:
13 hours
Step-by-step explanation:
8:00 plus 4 is twelve ( 12 o'clock )
then you have 9hrs left.
( 4+9=13 )
Question 1 (1 point)
Find the volume of a cube whose side length is 2.5 feet.
Volume
3
S
side 3
Answer:
Answer:
v=15.625ft³ or 15.63ft³
Step-by-step explanation:
v=s³
v=2.5³
v=15.625
round off to the nearest hundredth
v=15.63ft³
William drove 35 miles per hour for a total of 105 miles. He drove for x hours.
Which equation and solution below describe the situation?
Answer:
x=35 hrs
1 hour =105
cross mutiply
105÷35=3
The equation that describes the situation is 35x = 105.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The equations are of various types, such as Trigonometric equations, and quadratic equations.
William drove 35 miles per hour for a total of 105 miles.
The total miles William drove is 105 miles.
The speed at which he drove is 35 miles/ hour.
The total time he drove is given by x hours.
The equation has to be formed for this situation.
Speed is defined as the distance traveled with respect to time.
35 = 105 / x
35x = 105
This equation describes the given situation.
To know more about Equation
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4) half of 14
thank u
Answer:
7
Step-by-step explanation:
:)
it's so easy :))))))))
Answer:
Half of 14 is 7
Step-by-step explanation:
Sarah received a score of 36 points on an exam. The exam consisted of multiple choice questions that were worth 3 points for a correct answer and free response questions that were worth 5 points for a correct answer. If she answered a total of 10 questions correctly, how many of each type of question did she get correct?
Answer:
Sarah answered 7 multiple choice questions and 3 free response questions correctly.
Step-by-step explanation:
Given that: she has 36 points.
3 points each for the multiple choice question (MCQ)
5 points each for the free response question (FRQ)
To determine how many of each question was answered correctly. Let the number of MCQ she answered be represented by x and FRQ by y.
3x + 5y = 36 ............ 1
Since she answered a total of 10 question, then;
x + y = 10
x = 10 - y ................ 2
Substitute equation 2 into 1,
3(10 - y) + 5y = 36
30 - 3y + 5y = 36
2y = 6
y = 3
Substitute the value of y in equation 2,
x = 10 - y
= 10 - 3
= 7
x = 7, y = 3
Therefore, Sarah answered 7 multiple choice questions and 3 free response questions.
8^15÷8^−3 im lost i dont get this whole simply thing at all
8^15 ÷ 1/8^3 = 8^15 x 8^3=8^18
1.8014399e+16
Step-by-step explanation:
So before you can divide the numbers you have to simplify the exponents. You probably learned P(parentheses) E(exponents) M(multiply) D(divide) A(add) S(subtract.
PEMDAS is important because it shows you what order to so something in. Exponents is before divide so you simplify the exponents and you get 8^15= 3.5184372e+13 and 8^-3 = 0.001953125. So after you simplify the exponents you can now divide themNow (3.5184372e+13) ÷ (0.001953125) = 1.8014399e+16One serving of a certain brand of yogurt contains 7g of fat. The low-fat version contains 38.25% less fat per serving. How many grams of fat does one serving the low-fat yogurt contain?
Answer:
7g-100%
x-38,25
38,25*7:100=2,6775g
7g-2,6775g=4,4325g
Step-by-step explanation:
calculate the weight of a piece of steel to the nearest tenth of a pound. the diameter is 40" and the thickness is 2
Answer:
2513.3
Step-by-step explanation:
cylinder volume = π[tex]r^{2}[/tex]h
cylinder volume = π [tex]20^{2}[/tex](2)
cylinder volume = 2513.27
cylinder volume = 2513.3
write 7*7*7 in standard form
Answer:
Step-by-step explanation:
343
Answer:
7^3
Step-by-step explanation:
7 to the power of 3. Because there are 3, 7's so you are multiplying 7 3 times
help will give brainliest
Answer:
-10+4=-6
Step-by-step explanation:
Parallel lines /////////////
Answer:
38°
Step-by-step explanation:
∠4=∠2
∠2=∠6
∠6=38°
So ∠4=38°
Answer:
The answer is 38°
Step-by-step explanation:
When both lines are parallel, their vertical opposite angles will be the same. So ∠4 = 38°.
Write the equation of a line with a slope of 3 and passing through the point (-5, -7).
Show steps please
Answer:
y = 3x +8
Step-by-step explanation:
[tex](-5 ,-7)=(x_1,y_1) \\m = 3\\[/tex]
Plug in values into point-slope form
[tex]y -y_1 =m(x-x_1)\\y - (-7) = 3(x - (-5))\\y +7 =3(x+5)\\y+7 =3x+15\\y = 3x +15-7\\y = 3x +8[/tex]
Expresa el siguiente número 14322000000000000 en notación científica *
Answer:
14322 * 10¹²
1.4322 * 10¹⁶
Step-by-step explanation:
14322000000000000
14322 * 10¹²
1.4322 * 10¹⁶
Express the quotient 36/12
Answer:
Step-by-step explanation:
36/12 = 3
12 x 3 = 36
Find the area of the isosceles triangle.
Answer:
60in^2
Step-by-step explanation:
Area of a triangle = Height x Base X 1/2
Base = 10
Other 2 sides = 13
Now, let's split the Base into 2 parts.
=> 1 part = 5 and 2 part = 5
We can find the height using Pythagorean theorem
=> Isosceles triangle
=> (1 part of the base)^2 + Height^2 = The Hypotenuse^2 = the longer side of a triangle = 13^2
=> 5^2 + Height ^2 = 13^2
=> 25 + Height^2 = 169
=> 25 - 25 + Height ^2 = 169 - 25
=> Height^2 = 144
=> Height = Square root of 144
=> Height = 12
Area = 12 x 10 x 1/2
=> 12 x 5
=> 60 in^2
So, the Area is 60 in ^2
which of the following must describe an irrational number? (1pt) a number with a nonterminating decimal expansion a number with a non repeating decimal expansion a number with a repeating or terminating decimal expansion a number with a non repeating and non terminating decimal expansion.
Answer:
a number with a non repeating and non terminating decimal expansion.
Step-by-step explanation:
Irrational numbers are numbers which cannot be expressed as fractions, they are real numbers which cannot be expressed as rational numbers such as the square root of natural numbers other than perfect squares.
Irrational numbers are non repeating, non terminating decimal numbers with no group of the digits repeated. Therefore the decimal expansion does not terminate but continues without repetition example is π.
3x^2+11x+6 in factor form
Answer: (3x+2)(x+3)
Step-by-step explanation: Factor by grouping.
I hope this helps you out.
Answer:
[tex](3x+2)(x+3)[/tex]
Step-by-step explanation:
[tex]3x^{2} +11x+6[/tex]
Let's factor.
[tex]3x^{2}+11x+6[/tex]
This equals
[tex](3x+2)(x+3)[/tex]
Now you got your answer!
Hope this helps!
A three-person committee is chosen at random from a group of 8. How many different committees are possible?
Total hours worked for Hans Zupp is ___ .
a ) 40 hours 15 minutes
b ) 42 hours 35 minutes
c ) 44 hours 15 minutes
d ) 46 hours 15 minutes
Answer:
Option (D)
Step-by-step explanation:
Total hours worked of Monday= 4:45 hours + 5:00 hours = 9:45 hours
Total hours worked of Tuesday= 4:45 hours + 4:45 hours = 9:30 hours
Total hours worked of Wednesday= 4:30 hours + 4:30 hours = 9:00 hours
Total hours worked of Thursday= 4:45 hours + 4:15 hours = 9:00 hours
Total hours worked of Friday= 4:45 hours + 4:15 hours = 9:00 hours
Total hours worked = 9:45 + 9:30 + 9:00 + 9:00 + 9:00
= 46:15 hours
≈ 46 hours 15 minutes
Option (D) will be the answer.
evaluate 1/3(-15+3/2)
Answer:
-4 1/2
Step-by-step explanation:
1/3(-15+3/2)
1/3(-13 1/2)
1/3(-27/2)
-27/6
-4 3/6
-4 1/2
whats 5 less than 1 third
Answer:
-0.66666666666
Step-by-step explanation:
1/3-5/5
The sum of two numbers is 48. The larger number is 7 less than four times the smaller number. Find the numbers.
Answer:
Larger number = 37
Smaller Number = 11
Step-by-step explanation:
Lets take x as the bigger number and y as the smaller number
x + y = 48
What do we know?
The larger number is 7 less than four times the smaller number
so 4y - 7 = x
Lets replace the equation obove with x
4y - 7 + y = 48
5y - 7 = 48
5y = 48 + 7
y = 55/5
y = 11
Then multiply 11 by 4 11 times 4 = 44 and subtract by 7 44 - 7 = 37
To recheck add 37 to 11 and u should get 48