Answer:
[tex]90[/tex]
Step-by-step explanation:
Expand (3-9i)(3+9i) using the FOIL Method.
[tex]3 \times 3 + 3(9i) - 9i \times 3 - 9i(9i)[/tex]
Simplify and combine like terms.
[tex]90[/tex]
therefor, the answer is 90.
Several hours after departure the two ships described to the right are 50 miles apart. If the ship traveling south traveled 10 miles farther that the other how many miles did they each travel.
Answer:
[tex]Ship\ A = 40\ miles[/tex]
[tex]Ship\ B = 30\ miles[/tex]
Step-by-step explanation:
Given
[tex]d = 50[/tex] --- distance apart
[tex]Ship\ B = x[/tex]
[tex]Ship\ A = x + 10[/tex]
The question can be represented with the attached image.
Required
Solve for x
Using Pythagoras theorem, we have:
[tex]x^2 + (x + 10)^2 = 50^2[/tex]
Open bracket
[tex]x^2 + x^2 + 20x + 100 = 2500[/tex]
Collect like terms
[tex]x^2 + x^2 + 20x + 100 - 2500 = 0[/tex]
[tex]2x^2 + 20x -2400 = 0[/tex]
Divide through by 2
[tex]x^2 + 10x -1200 = 0[/tex]
Expand
[tex]x^2 + 40x - 30x -1200 = 0[/tex]
Factorize
[tex]x(x + 40) - 30(x +40) = 0[/tex]
Factor out x + 40
[tex](x - 30)(x +40) = 0[/tex]
Split and solve for x
[tex]x - 30 = 0\ or\ x + 40 = 0[/tex]
[tex]x = 30\ or\ x = -40[/tex]
Distance can not be negative
So:
[tex]x = 30[/tex]
Recall that:
[tex]Ship\ B = x[/tex]
[tex]Ship\ A = x + 10[/tex]
This implies that:
[tex]Ship\ B = 30\ miles[/tex]
[tex]Ship\ A = 30 + 10\ miles[/tex]
[tex]Ship\ A = 40\ miles[/tex]
Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 51 people is taken. Step 1 of 2 : What is the probability of a random person on the street having an IQ score of less than 98? Round your answer to 4 decimal places, if necessary.
Answer:
0.4470 = 44.70% probability of a random person on the street having an IQ score of less than 98.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability of a random person on the street having an IQ score of less than 98?
This is the pvalue of Z when X = 98. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{98 - 100}{15}[/tex]
[tex]Z = -0.1333[/tex]
[tex]Z = -0.1333[/tex] has a pvalue of 0.4470
0.4470 = 44.70% probability of a random person on the street having an IQ score of less than 98.
Carmen runs each lap in 4 minutes. She will run less than 28 minutes today. What are the possible numbers of laps she will run today?
Answer:
# of laps < 28, the number of laps will be less than 28.
1 lap = 4 minutes
28 laps = 112 minutes
Because we want less than 28 laps,
27 laps = 108 minutes
She can run any amount of laps less than 28.
a slice of a right square pyramid perpendicular to its base but not through its top vertex
A. Square
B. Trapezoid
Answer:
This is a trapezoid.
Step-by-step explanation:
Another area and perimeter question!!!
Pls helppppp
Answer:
D. 62 inches
Step-by-step explanation:
the object is symmetrical across z, so the lengths on the other side will be the same as x and y
the perimeter would just be 2x + 2y = 2(12) + 2(19) = 62 inches
Function f is differentiable and decreasing for all real numbers. If y=f(2x^3 - 3x^2), for which of the following intervals of x will the value of y NOT be decreasing?
Answer:
The terai region extends from the chure range in the north to the border of India in the south.lt covers 17 percent of total land of Nepal .this terai region is mostly flat and plain with alluvial fertile deposited by the rivers . the climate of the reason is hot and wet in summer and cold and dry in winter.Terai also called the granary of Nepal as more than half percent of people of Nepal depend on the vegetation of Terai region. Terai is plain, where more cultivation is possible. Cultivation is impossible in mountain region due to difficult topography and temperate region and even in hilly region with lots of vegetation it's not possible due to slope area. Terai is only the possible region where much cultivation is possible. Different kinds of vegetation, valuable medicinal herbs, important trees, etc. are found in Terai region. So, Terai region is called the granary of Nepal.The terai region extends from the chure range in the north to the border of India in the south.lt covers 17 percent of total land of Nepal .this terai region is mostly flat and plain with alluvial fertile deposited by the rivers . the climate of the reason is hot and wet in summer and cold and dry in winter.Terai also called the granary of Nepal as more than half percent of people of Nepal depend on the vegetation of Terai region. Terai is plain, where more cultivation is possible. Cultivation is impossible in mountain region due to difficult topography and temperate region and even in hilly region with lots of vegetation it's not possible due to slope area. Terai is only the possible region where much cultivation is possible. Different kinds of vegetation, valuable medicinal herbs, important trees, etc. are found in Terai region. So, Terai region is called the granary of Nepal.The terai region extends from the chure range in the north to the border of India in the south.lt covers 17 percent of total land of Nepal .this terai region is mostly flat and plain with alluvial fertile deposited by the rivers . the climate of the reason is hot and wet in summer and cold and dry in winter.Terai also called the granary of Nepal as more than half percent of people of Nepal depend on the vegetation of Terai region. Terai is plain, where more cultivation is possible. Cultivation is impossible in mountain region due to difficult topography and temperate region and even in hilly region with lots of vegetation it's not possible due to slope area. Terai is only the possible region where much cultivation is possible. Different kinds of vegetation, valuable medicinal herbs, important trees, etc. are found in Terai region. So, Terai region is called the granary of Nepal.
Arc measure of A and B
Answer:
arc a = 64°
arc b = 112°
Step-by-step explanation:
inscribed angles = 1/2 their arc
arc of 102° = 204° arc
arc a = 204° - 140° = 64°
arc of 92° = 184°
arc b = 360° - 184° - 64° = 112°
answer this asap I'm desperate :( ...we both were sweating like two pigs" is an example of...
allusion
metaphor
hyperbole
simile
Answer:
sorry
Step-by-step explanation:
don't know I m in 8th
I will surely help you
Answer:
Simile
Step-by-step explanation:
A simile is a figure of speech that directly compares two things. Similes differ from other metaphors by highlighting the similarities between two things using comparison words such as "like", "as", "so", or " than", while other metaphors create an implicit comparison.
Hope this helps! If you have any questions revolving around this topic,feel free to ask me and I will be happy to help!
Can you guys help? It’s writing an equation of line given.
Answer:
Step-by-step explanation:
y = - x - 4 (slope-intercept form)
x + y = - 4 (standard form)
alonzo has a job and makes 13.50 per hour he works 9 hours how much money does he take home
A ball is tossed into the air. The quadratic function
h(t) = -16t2 + 14t + 5 represents the situation, where t
represents the time, in seconds, after the ball is tossed
and h(t) represents the height of the ball, in feet. Which
of the following statements is NOT true?
Answer: The leading coefficient indicates that the graph of the parabola that represents the ball’s height over time will open in an upward direction
Step-by-step explanation:
find the value f(-5)
Answer:
-9
Step-by-step explanation:
The sum of 2 numbers is 11 and the difference is 5
Answer:
let no. be x and y.
we have
x+y=11.......(1)
x-y=5........(2)
adding equation 1&2
x+y+x-y=11+5
2x=16
x=16/2=8
again
8-y=5
y=8-5=3
:.
x=8,y=3
Sally's bank account had a balance of 230 at the beginning of the month. She had two deposits of 50 and 420 and just one withdrawal of 190. Her balance at the end of the month was $______ ?
Answer:
510
Step-by-step explanation:
Sally bank account had a beginning balance of 230
She made two deposits of 50 and 420
50+420
= 470
She made a withdrawal of 190
Therefore her balance at the end of the month can be calculated as follows
470+230
= 700
= 700-190
= 510
Hence the balance at the end of the month is 510
Consider the following IP problem.
Max z = 5x1+x2
s.t. − x1 + 2x2 ≤ 4
x1 − x2 ≤ 1
4x1 + x2 ≤ 12
x1,x2 ∈Z+
1. Solve graphically
2. Solve the LP relaxation of the problem graphically. Round this solution to the nearest integer solution and check whether it is feasible. Then enumerate all the rounded solutions by rounding this solution for the LP relaxation in all possible ways (i.e., by rounding each non-integer value both up and down). For each rounded solution, check for feasibility and, if feasible, calculate z. Are any of these feasible rounded solutions optimal for the IP problem?
Answer:
See Annex
Step-by-step explanation:
The relaxation of any Linear Programming problem, consists of eliminating the integer constraint condition, keeping the original constraint and the objective function, solving the problem as continuous variables. If in such new condition we find that optimal solution consist of integer solution we have found optimal solution already, if not we need to go ahead with the branching procedure of making variables integer above and down of the fractional values.
In this particular case ( see GeoGebra graphic solution attached changing x₁ and x₂ by x and y respectively ), and Objective Function in red we got integer solution :
z(max) = 11
x₁ = x = 2
x₂ = y = 1
Which value is included in the solution set for the inequality graphed on the number line?
4
3
2
-1
0 1 2
3
4
-5
O
-2.
ОО
03
Answer:
-5
Step-by-step explanation:
The number line is saying that the solution could be any number less than -2.
The value included in the solution set for the inequality graph on the number line is -5.
How to find the solution set of inequality graph on a number line?
The number line represents an inequality graph.
Let's use the range of value on the graph as x.
Therefore, the inequality on the number line will read as follows:
x < -2
Hence,
x less than -2 includes -3, -4, -5, -6, -7, -8 ..
Therefore, the value included in the solution set for the inequality graph on the number line is -5.
learn more on inequality graph here: https://brainly.com/question/1400037
What is the mean of the following data set? 6, 7, 3, 8, 6, 6, 2, 9, 7 A 8 B 9 C 6 D 7
Answer:
The mean is 6.
Step-by-step explanation:
A cell phone company is offering a plan for unlimited talk and text with an additional charge for data that can be represented by the function C(g) = 14.99g + 32, where C represents the cost, in dollars, and g represents the number of gigabytes of data, According to this model, fill in the blanks with the values that complete the sentence. The cost of the plan for unlimited talk and text is $ ______ , with an additional cost of $ ______ for each gigabyte of data.
This means that the extra cost for using 1 gigabyte of data will be $14.99, for using 2 gigabytes of data it will be $29.98, and so on.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
The given function C(g) = 14.99g + 32 represents the cost, in dollars, for a cell phone plan that offers unlimited talk and text, with an additional charge for data usage.
The function has two parts:
The fixed cost of the plan is $32 (this is the cost you pay even if you don't use any data).
The variable cost of the data usage is $14.99 per gigabyte.
So, the cost of the plan for unlimited talk and text is the fixed cost, which is $32.
And, the additional cost for each gigabyte of data is the variable cost, which is $14.99.
This means that if you use 1 gigabyte of data, the additional cost will be $14.99, if you use 2 gigabytes of data, the additional cost will be $29.98, and so on.
Learn more about algebraic Expression here:
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Ice cream: A certain ice cream parlor offers fifteen flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors.
Part 1 of 2
In how many ways can you choose a cone if it matters which flavor is on top, which is in the middle and which is on the bottom?
de
The number of ways to choose a cone, if order matters, is
Answer:
The number of ways to choose a cone, if order matters, is 45.
Step-by-step explanation:
Given that a certain ice cream parlor offers fifteen flavors of ice cream, and you want an ice cream cone with three scoops of ice cream, all different flavors, to determine in how many ways you can choose a cone if it matters which flavor is on. top, which is in the middle and which is on the bottom, the following calculation must be performed:
15 x 3 = X
45 = X
The number of ways to choose a cone, if order matters, is 45.
How do the temperatures compare? Order the temperatures from coldest to warmest
52°F
51.8°F
37.3°F
-17°F
-43.6°F
-37.4'F
which order
Answer:
-43.6° F, -37.4° F, -17° F, 37.3° F, 51.8° F, 52° F
Step-by-step explanation:
The greater the number, the warmer the temperature.
Draw an equilateral triangle of perimeter 10 centimetres.
Answer:
See attachment for triangle
Step-by-step explanation:
Given
Shape: Equilateral triangle
[tex]Perimeter = 10cm[/tex]
Required
Draw the triangle
First, we determine the side lengths.
The perimeter of an equilateral triangle is:
[tex]Perimeter = 3 * Length[/tex]
So, we have:
[tex]10= 3 * Length[/tex]
Solve for Length
[tex]Length = \frac{10}{3}[/tex]
[tex]Length = 3.33[/tex]
See attachment for triangle
Does anyone know the answer to this?
Answer:
x=18 and y=106
Step-by-step explanation:
Let's say you have a 4 gallon and a 10 gallon pailHow can you measure exactly 2 gallons of water?
You can fill the 10 gallon pail all the way up. After that, you can pour the water from the 10 gallon pail, into the 4 gallon pail 2 times. That will leave you with 2 gallons in the 10 gallon pail.
Which set of numbers is ordered from least to greatest?
Answer:
B.3.2 ,3.317 ,3.606 ,3.61.
Step-by-step explanation:
i guess that is the answer,but if it isn't tell me I may try it again.good day.
Write a decimal that is less than 3.45 but greater than 3.0. helppp!
Answer:
any decimal between 3.0 and 3.45. You can,use 3.25 if u don't wanna think about it
Answer:There are mutipal answers but here’s one 3.1
Step-by-step explanation:
What is the simplest form of 1/6 divided by 2
Answer:
1/12
hope this helps
have a good day :)
Step-by-step explanation:
The solution is 1/12 , is the simplest form of 1/6 divided by 2.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
1/6 divided by 2
i.e. 1/6÷ 2
=1/6* 1/2
=1/12
Hence, The solution is 1/12 , is the simplest form of 1/6 divided by 2.
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Find the volume of a pyramid with a square base, where the perimeter of the base is 16.1 ft and the height of the pyramid is 12.1 ft. Round your answer to the nearest tenth of a cubic foot?
Answer: V= 65.3 ft^3
A closet in the shape of a rectangular prism is 2 feet deep, 5 feet wide, and 7 feet tall. What is the volume of the closet in cubic feet?
Answer:
70 cm
Step-by-step explanation:
Answer:
70 cubic feet
Step-by-step explanation:
First step is to multiply the 2 feet deep by th 5 feet wide. which is also written as:
2*5=10
Next multiply 10 by the 7 feet tall. You can write this like:
10*7=70
70 cubic feet is the answer
In the diagram, △NPQ ∼ △NLM and PL = 8.
a. Find the value of x
b. Find the lengths NP and NL, rounding to the nearest hundredth.
NP =
and NL =
Answer:
x = 14
NP = 3.66
NL = 8.01
Step-by-step explanation:
since △NPQ ∼ △NLM
<L = <P
3x + 18 = 60
3x = 60 - 18
3x = 42
x = 42/3
x = 14
Similarly;
PN/PL = QN/QM
y/8 = 3.2/7
Cross multiply
7y = 3.2* 8
7y = 25.6
y = 25.6/7
y = 3.66
Hence NP = 3.66
Also
NP/NQ = NL/NM
3.66/3.2 = NL/7
3.2NL = 7 * 3.66
3.2NL = 25.62
NL = 25.62/3.2
NL = 8.01
Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle. The value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).
Given information-The given tingle NPQ and triangle NLM are the similar triangle.
The length of the line PL is 8 cm.
Similar triangle-Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle.
Value of the x-
As the two triangle are similar triangle, thus the length of the angle P is equal to the angle L. Therefore,
[tex]\angle L =\angle P\\ [/tex]
Keep the value of the angle from the diagram,
[tex]\begin{algined}\\ 3x+18&=60\\ 3x&=60-18\\\\ 3x&=42\\ x&=\dfrac{42}{3} \\ x&=14\\ \end[/tex]
Thus the value of the x is 14.
The length of the NP.
In the similar triangle the following ratios are equal,
[tex]\dfrac{PN}{PL} =\dfrac{QN}{QM} [/tex]
Put the values from the diagram,
[tex]\begin{aligned} \dfrac{y}{8}&=\dfrac{3.2}{7} \\ y&=\dfrac{3.2}{7} \times 8\\ y&=3.66\\ \end[/tex]
Value of y is equal to the length NP. Hence the length of the NP is equal to the 3.66 cm.
The length of the NL-
In the similar triangle the following ratios are equal,
[tex]\dfrac{NP}{NQ} =\dfrac{NL}{NM} [/tex]
Put the values from the diagram,
[tex]\begin{aligned} \dfrac{3.66}{3.2}&=\dfrac{NL}{7} \\ NL&=\dfrac{3.66}{3.2} \times 7\\ y&=8.01\\ \end[/tex]
Thus the length of the NL is equal to the 8.01 cm.
Hence the value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).
Learn more about the similar triangle here;
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There are 150 people in the library. If 60 of them are girls, what percent of the people in the library are girls?
Answer:
40% are girls
Step-by-step explanation:
60/150=0.4=40%