Answer
Step-by-step Explanation
In the expansion of variables in a bracket raised to a particular power, we either use the Binomial theorem or the Pascal's triangle.
The Binomial theorem teaches how to use permutaion and combination to obtain the coefficients of each term while the Pascal's triangle presents the coefficient of each term for different integer powers of the variables in a triangular form where the next line of the triangle can be obtained from the previous line just by starting with a 1 and adding two consecutive terms of that previous line and ending with 1.
Can you please help me
The figure given is a sphere
A surface area of a sphere is given by
[tex]A=4\pi r^2[/tex]The diameter of the sphere is given to be 42 cm
The radius of the sphere is half the diameter =
[tex]r=\frac{42}{2}=21\operatorname{cm}[/tex]Substituting the value of r into the formula
[tex]\begin{gathered} A=4\times\pi\times21^2 \\ A=5541.8\operatorname{cm}^2 \end{gathered}[/tex]The correct answer is option A
Containers R Us purchased 5 dozen work gloves for $73.80. How much did each pair of gloves cost?
In order to determine the price of each pair, just calculate the quotient in between the total price and the number of dozen works, which were 5:
73.80/5 = 14.76
Hence, each pair of dozen work costed $14.76
What represents the values of the range in the following graph?A.the range is represented by the average growth of the horse. B. The range is represented by cm/year.C. The range is represented by the height of the horse.D. The range is represented by the age.
The range is the set of possible output values, which are shown on the y-axis.
As shown in the graph, the range is represented by the average growth of the horse.
Therefore, the answer is letter A.
Answer:
A.the range is represented by the average growth of the horse.
Step-by-step explanation:
Writing an equation in slope intercept form for the line passing through each pair of points. (0,3) (1,-2)
Calculating the slope of the line with points (0,3) (1,-2)
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1}=\frac{-2-3}{1-0}=\frac{-5}{1}=-5 \\ m=-5 \end{gathered}[/tex]With the slope and one of the points we find the y-intercept with the equation y=mx +b.
y= mx + b (m: slope , b=y-intercept)
3=-5(0) + b (Replacing m=-5 and the point (0,3))
3= 0 + b (Multiplying)
3=b
The answer is y=-5x + 3.
A boat is heading towards a lighthouse, whose beacon-light is 108 feet above the water. From pointA, the boat’s crew measures the angle of elevation to the beacon, 8 degrees, before they draw closer. They measure the angle of elevation a second time from pointB at some later time to be 16∘. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Given: The information of a boat heading towards a lighthouse
To Determine: The distance from point A to point B
Solution: The information provided can be translated into the diagram below
[tex]\begin{gathered} m\angle ADC+m\angle DAC=90^0 \\ m\angle ADC+8^0=90^0 \\ m\angle ADC=90^0-8^0 \\ n\angle ADC=82^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle BDC+m\angle DBC=90^0 \\ m\angle BDC=90^0-m\angle DBC \\ m\angle BDC=90^0-16^0 \\ m\angle BDC=74^0 \end{gathered}[/tex]Using SOH CAH TOA
[tex]\begin{gathered} \tan 74^0=\frac{BC}{108} \\ BC=108\tan 74^0 \\ BC=108\times3.4874 \\ BC=376.64ft \\ BC\approx377ft(nearest\text{ foot)} \end{gathered}[/tex][tex]\begin{gathered} \tan 82^0=\frac{AC}{108} \\ AC=108\times\tan 108 \\ AC=108\times7.115 \\ AC=768.4599 \end{gathered}[/tex][tex]\begin{gathered} AB=AC-BC \\ AB=768.45993-376.64 \\ AB=391.8199 \\ AB\approx392ft \end{gathered}[/tex]Hence, the distance from point A to point B is 392ft (nearest foot)
The volume of a gas, such as helium or air, varies inversely with the pressure on it. If the volume of air is 325 cubic inches under a pressure of 11 psi, what pressure has to be applied to decrease the volume to 143 cubic inches?
ANSWER
The pressure is 25 psi
STEP-BY-STEP EXPLANATION:
From the question provided, you can see that the relationship between the volume of a gas and the pressure is an inverse relationship.
The volume of a gas varies inversely with the pressure on it
This implies that as the volume of the gas increases the pressure of the gas decreases and vice versa.
The next thing is to assign variables
Let the volume of the gas be V
Let the pressure of the gas be P
Mathematically, this can be represented as
[tex]\begin{gathered} V\text{ }\propto\text{ }\frac{1}{P} \\ \text{Introduce a proportionality constant K} \\ V\text{ = }\frac{K}{P} \\ \text{Cross multiply} \\ K\text{ = VP -------- equation 1} \\ \end{gathered}[/tex]The next step is to find the value of K from the given information in the question
• Volume = 325 cubic inches
,• Pressure = 11 psi
Recall that, K = VP
K = 325 * 11
K = 3,575
Since you have gotten the value of K, then, you can now find your pressure when the volume Is 143 cubic inches
[tex]\begin{gathered} V=143inches^3 \\ K\text{ = 3,575} \\ K\text{ = VP} \\ \text{Divide both sides by V} \\ \frac{K}{V}\text{ = }\frac{VP}{V} \\ P\text{ = }\frac{K}{V} \\ P\text{ = }\frac{3575}{143} \\ P\text{ = 25 ps}i. \end{gathered}[/tex]Hence, the pressure is 25 psi
Elan is painting the outside of a rectangular barn door. It is 80 inches high and 60 inches wide. What is the area of the outside door?
Draw the barn dorr
the area of a rectangle is
[tex]A=h\times w[/tex]where h is height and w the width
the replacing
[tex]\begin{gathered} A=80\times60 \\ A=4800 \end{gathered}[/tex]then area of outside dor is 4800 square inches
John bought a 20 pound bag of dog food. He feeds his dog twice a day. If John gives his dog 3/4 pound of dog food each feeding, how many days will it last?
Total weight of the bag of dog food bought by John = 20 Pounds
Number of times the dog is fed in a day = 2
Weight consumed by the dog at each feeding = 3/4 Pound.
Therefore:
[tex]\begin{gathered} \text{Weight of food used per day = 2 }\times\frac{3}{4}\text{ } \\ =\frac{6}{4} \\ =\frac{3}{2}\text{ Pounds} \end{gathered}[/tex]To determine how many days the 20-pound bag will last, we have:
[tex]\begin{gathered} \frac{20\text{ Pounds}}{\frac{3}{2}\text{ Pounds per day}} \\ =20\times\frac{2}{3} \\ =\frac{40}{3} \\ =13\frac{1}{3}\text{ days} \end{gathered}[/tex]The 20-pound bag of dog food will last 13 1/3 days.
What change do you have to make to the graph?
EXPLANATION:
Given;
We are given the function below;
[tex]f(x)=3^x[/tex]Required;
We are required to describe what change would be made to graph the function;
[tex]g(x)=3^{x-7}[/tex]For a function given such as the one here, when the graph is shifted to the right, then the original function is affected as follows;
[tex]\begin{gathered} f(x)=x \\ \\ Shift\text{ }to\text{ }the\text{ }right: \\ f(x)+(x)=x \\ \\ Subtract\text{ }(x)\text{ }from\text{ }both\text{ }sides: \\ f(x)+(x)-(x)=x-(x) \\ \\ f(x)=x-(x) \end{gathered}[/tex]For a shift to the left, we would have a plus sign, that is, add x number of units the graph is being shifted.
Therefore, for a function that has changed such as the one given,
[tex]g(x)=3^{x-7}[/tex]What we have is shift the original graph 7 units to the right.
ANSWER:
[tex]Shift\text{ }the\text{ }graph\text{ }7\text{ }units\text{ }right[/tex]The first option is the correct answer.
Mr. Nguyen bought a suit that was on sale for 40% off the original price. He paid 9% salea tax on the sake price. The original price of the suit was $260. How much did he pay for the suit, including tax, to the nearest dollar?
The original price of the suit was $260. If the sale price was 40% off the original price, it means that the amount of discount was
40/100 * 260 = 104
The sale price is 260 - 104 = $156
If he paid sales tax of 9% of the sale price, it means that the amount of tax is
9/100 * 156 = 14.04
Therefore, the amount that he paid including tax is
156 + 14.04 = $170.04
Rounding up to the nearest dollar, the amount is $170
Find the measure of base of the following parallelogram shown below.Area =10.92 cm?2.6 cmAnswer:cm
The area of a paralllelogram can be found by multiplying its base with its height. In this problem we were given the area and the height, therefore we can solve for the base as shown below.
[tex]\begin{gathered} Area=base\cdot height \\ ase=\frac{Area}{height} \\ base=\frac{10.92}{2.6} \\ base=4.2\text{ cm} \end{gathered}[/tex]The base of the parallelogram is 4.2 cm
The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.A. 4, 5, 6B. 11, 12, 15
To find out if a triangle is acute, right or obtuse we need to use the following rules:
[tex]\begin{gathered} a^2+b^2>c^2\Rightarrow acute \\ a^2+b^2=c^2\Rightarrow right\text{ } \\ a^2+b^2where c is the largest side of the triangle and a and b are the other two sides.A.
In this case c=6 and we can take the other two as a=4, b=5. Then:
[tex]\begin{gathered} 4^2+5^2?6^2 \\ 16+25\text{?}36 \\ 41>36 \end{gathered}[/tex]Therefore triangle A is an acute triangle.
B.
In this case c=15, b=12 and a=11. Then:
[tex]\begin{gathered} 11^2+12^2?15^2 \\ 121+144\text{?}225 \\ 265>225 \end{gathered}[/tex]Therefore triangle B is an acute triangle.
Find the odds in favor of getting an extra turnWhat is the probability of choosing a lemon-flavored piece
Given:
Probability of few cases is given
Required:
I would appreciate your feedback - you can provide it by rating the session.
Explanation:
(a)
[tex]\begin{gathered} the\text{ odds in favor of getting an extra turn=} \\ \\ =\frac{probability\text{ of chances to get an extra turn in 17 attempts}}{probability\text{ of chance to not get an extra turn in 17 attempts}} \\ \\ =\frac{6}{17-6}\text{ =}\frac{6}{11} \end{gathered}[/tex](b) Odds against is given by number of failures/number of successes
[tex]\begin{gathered} \frac{no\text{ of failures }}{no\text{ of success}}=\frac{9}{10} \\ \\ The\text{ total number of trials in failures+number of successes= 9+10=19} \\ \\ So\text{ getting a lamon-flavored piece is a success.} \\ \\ p(getting\text{ a lamon flavoured piece\rparen=}\frac{10}{19} \end{gathered}[/tex]Required answer:
[tex](a)\frac{6}{11}\text{ \lparen b\rparen}\frac{10}{19}[/tex]what is the standard deviation of the following data set rounded to the nearest tenth
The general formula for the standard deviation is:
[tex]\sigma=\sqrt{\frac{\Sigma(x_i-\mu)^2}{N}}[/tex]in which, N is the number of data, and μ is the sample's mean.
Start by calculating the sample's mean
[tex]\begin{gathered} \mu=\frac{7.7+8.4+9+8+6.9}{5} \\ \mu=8 \end{gathered}[/tex]then, apply the standard deviation formula
[tex]\begin{gathered} \sigma=\sqrt{\frac{(7.7-8)^2+(8.4-8)^2+(9-8)^2+(8-8)^2+(6.9-8)^2}{5}} \\ \\ \sigma=\sqrt{\frac{(-0.3)^2+(0.4)^2+(1)^2+(0)^2+(-1.1)^2}{5}} \\ \\ \sigma=\sqrt{\frac{2.46}{5}} \\ \\ \sigma=\sqrt{0.492} \\ \sigma=0.701\approx0.7 \end{gathered}[/tex]Answer:
The standard deviation is 0.7
In a parallelogram, two adjacent sides are 2.c – 7 and 3x – 6. If the perimeter of the parallelogram is 34, find x and the shorter side of the parallelogram X= Shorter Side =
Given the information on the problem, we have the following parallelogram:
since the perimeter is 34, we can write the following equation:
[tex]2(3x-6)+2(2x-7)=34[/tex]solving for x, we get:
[tex]\begin{gathered} 2(3x-6)+2(2x-7)=34 \\ \Rightarrow6x-12+4x-14=34 \\ \Rightarrow10x-26=34 \\ \Rightarrow10x=34+26=60 \\ \Rightarrow x=\frac{60}{10}=6 \\ x=6 \end{gathered}[/tex]now that we have that x = 6, we can find the measure of the sides:
[tex]\begin{gathered} x=6 \\ 3(6)-6=18-6=12 \\ 2(6)-7=12-7=5 \end{gathered}[/tex]therefore, x = 6 and the shorter side measures 5 units
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the probability that 2 - a randomly selected adult has an IQ between 100 and 120?
ANSWER
[tex]\begin{equation*} 0.40824 \end{equation*}[/tex]EXPLANATION
We want to find the probability that a randomly selected adult has an IQ between 100 and 120.
To do this, first, we have to find the z-score for 100 and 120 using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = IQ score
σ = standard deviation
μ = mean
Hence, for an IQ score of 100, the z-score is:
[tex]\begin{gathered} z=\frac{100-100}{15}=\frac{0}{15} \\ z=0 \end{gathered}[/tex]For an IQ score of 120, the z-score is:
[tex]\begin{gathered} z=\frac{120-100}{15}=\frac{20}{15} \\ z=1.33 \end{gathered}[/tex]Now, to find the probability of an IQ score between 100 and 120, apply the formula:
[tex]\begin{gathered} P(100Using the standard normal table, we have that:[tex]\begin{gathered} P(z<1.33)=0.90824 \\ P(z<0)=0.5 \end{gathered}[/tex]Therefore, the probability is:
[tex]\begin{gathered} P(0That is the answer.The force of the wind blowing on a window positioned at a right angle to the direction of the wind varies jointly as the area of the window and the square of the wind's speed. It is known that a wind of 30 miles per hour blowing on a window measuring 4 feet by 5 feet exerts a force of 150 pounds. During a storm with winds of 60 miles per hour, should hurricane shutters be placed on a window that measures 3 feet by 4 feet and is capable of withstanding 300 pounds of force?
We have the following:
The force of wind: F = 150 pounds
The square of the winds speed: V = 30 miles per hour
The area of the windows: A = 4*5 = 20 square feet
The formula is:
[tex]F=kAV^2[/tex]replacing:
[tex]\begin{gathered} 150=k\cdot20\cdot30^2 \\ k=\frac{150}{20\cdot900} \\ k=\frac{1}{120} \end{gathered}[/tex]now, the force of wind with 60 miles per hour and 12 (3*4) square feet
[tex]\begin{gathered} F=\frac{1}{120}\cdot12\cdot60^2 \\ F=360_{} \end{gathered}[/tex]The answer is 360 pounds
Determine the angle measures of quadrilateral EFGH that would result in it's similarity to quadrilateral ABCD
Solution:
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1.
Similarity statement:
In geometry, it states that two sides are similar if they have the same side ratio and the same angles
From the image in the question,
The quadrilateral ABCD has the following angles
[tex]\begin{gathered} m\angle A=90^0 \\ m\angle B=132^0 \\ m\angle C=73^0 \\ m\angle D=65^0 \end{gathered}[/tex]From the similarity statement above,we can deduce that
[tex]undefined[/tex]Based on the graphs of f (x) and g(x), in which interval(s) are both functions increasing?Polynomial function f of x, which increases from the left and passes through the point negative 4 comma negative 4 and goes to a local maximum at negative 3 comma 0 and then goes back down through the point negative 2 comma negative 2 to a local minimum at the point negative 1 comma negative 4 and then goes back up through the point 0 comma 0 to the right, and a rational function g of x with one piece that increases from the left in quadrant 2 asymptotic to the line y equals 1 passing through the points negative 6 comma 2 and negative 2 comma 6 that is asymptotic to the line x equals negative 1 and then another piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 1 passing through the point 0 comma negative 4 and 4 comma 0 that is asymptotic to the line y equals 1(–°, –3) ∪ (–1, °)(–°, –3) ∪ (4, °)(–°, –3)(–°, °)
Increasing intervals for f(x) and g(x); A function is incrasing when the y-value increases as the x-value increases.
f(x) and g(x) increases in two intervals (x-intervals):
From negative infinite to -3
From -1 to infinite
[tex](-\infty,-3)\cup(-1,\infty)[/tex]Both intervals are increasing through (-∞,-3) U (-1,∞)
Need to find circumference of the circle. Use 3.14 for the value of pi. m let diameter = 20 in
the circumference of the circle is 62.8 inches
Explanation
the circumference of a circle is given by:
[tex]\text{Circumference(C)}=\text{ Diameter(D)}\cdot\pi[/tex]Step 1
Let
[tex]\begin{gathered} \pi=3.14 \\ \text{Diameter}=\text{ 20 in} \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} \text{Circumference(C)}=\text{ Diameter(D)}\cdot\pi \\ C=\text{ 20in }\cdot3.14 \\ C=62.8\text{ inches} \end{gathered}[/tex]therefore, the circumference of the circle is 62.8 inches
I hope this helps you
Write the equation for each line in slope - intercept form:Y int: 4 and goes through (1,8)
Okay, here we have this:
Considering that the slope intercept form is the following:
y=mx+b
If we replace with the provided info we obtain the following:
8=m(1)+4
And here we can clear for the slope (m):
8=m(1)+4
8=m+4
m=8-4
m=4
With this slope we can replace in the slope intercept form and finally we obtain the following equation:
find the unit price and round your answer to the nearest cent. you make $512.92 a week. if you work 36 hours find your hourly rate of pay
EXPLANATION
Given that we make $512.92 by week and we work 36 hours, we can apply the unitary method in order.
[tex]\text{hourly rate=}\frac{512.92\text{ dollars}}{36\text{ hours}}=14.25\text{ }\frac{dollars}{\text{hour}}[/tex]In conclusion, the hourly rate is 14.25 dollars.
Suppose that you borrow $14,000 for five years at 6% toward the purchase of a car. Find the monthly payment and the total interest for the loan.
We have to calculate the monthly payments (number of subperiods per year n = 12) for a loan of $14,000 (P = 14000) for five years (t = 5) at an interest rate of 6% (r = 0.06).
We can use the annuity formula to calculate the monthly payment (PMT) as:
[tex]\begin{gathered} \text{PMT}=\frac{P(\frac{r}{n})}{\lbrack1-(1+\frac{r}{n})^{-nt}\rbrack} \\ \text{PMT}=\frac{14000\cdot(\frac{0.06}{12})}{\lbrack1-(1+\frac{0.06}{12})^{-12\cdot5}\rbrack} \\ \text{PMT}=\frac{14000\cdot0.005}{\lbrack1-1.005^{-60}\rbrack} \\ \text{PMT}\approx\frac{14000\cdot0.005}{1-0.74137} \\ \text{PMT}\approx\frac{70}{0.25863} \\ \text{PMT}\approx270.66 \end{gathered}[/tex]Answer: the monthly payments will be $270.66
I need help in this math assignment thank you! :)
Answer: l = 25g
Explanation:
From the information given,
He ties 25 inches of ribbon around each gift.
(g) represents the number of gifts and (r) represents the length of ribbon used. This means that the length of ribbon tied around g gifts is 25g. Thus, the function representing the relationship between the length of ribbon and the number of gifts is
l = 25g
ma ate one slice of pizza, pa ate 2 pizza slices how much pizza did they eat together, what percent of the pizza is not eaten?
According to the given data we have the following:
ma ate one slice of pizza
pa ate 2 pizza slices
Therefore, if there are 8 slices of pizza, the amount of pizza thay they ate together would be calculated as follows:
amount of pizza thay they ate together= number of pieces that they ate together/The total number of pieces
amount of pizza thay they ate together=3/8
amount of pizza thay they ate together=0.375
Therefore to calculate the amount of pizza that is not eaten we would have to make the following calculation:
amount of pizza that is not eaten=1-0.375
amount of pizza that is not eaten=0.625
Therefore, the percent of the pizza is not eaten is 62.5%
Use the following words to complete the sentences : 1) Run, 2) Positive , 3) Constant , 4) Linear , 5) Steepness ,6) Vertical 7) Horizontal ,8) Rise 9) Negative , 1) Slope is the ----- of a line. It is also know as the ------ rate of change. 2) If a line is slanting upwards we say it has a ------ slope. If a line is slanting downwards we say it has a ------ slope .3) A slope of zero means the line is ----- .4) An undefined slope means the line is ----- . 5) All straight line graphs are known as ------ relationships .6) To find the slope of a line we use the formula ----- over ------ .
1) Slope is the ----- of a line. It is also known as the ------ rate of change.
Slope means steepness and it is a constant rate of change meaning that it does not change.
2) If a line is slanting upwards we say it has a ------ slope.
Slanting upward means a positive slope, for example when you are moving uphill.
If a line is slanting downwards we say it has a ------ slope
Slanting downward means a negative slope, for example when you are moving downhill.
3) A slope of zero means the line is -----
a Slope of 0 means that the line is horizontal. for example when you are moving on a straight road.
4) An undefined slope means the line is -----
An undefined slope means that the line is vertical. for example when you are climbing a vertical wall.
5) All straight line graphs are known as ------ relationships.
They are known as linear relationships.
6) To find the slope of a line we use the formula ----- over ------
We use the slope formula that is rise over run.
A person collected $1,400 on a loan of $1,200 they made 7 years ago. If the person charged simple interest, what was the rate of interest?
Solution:
The formula that we can apply in this case is the following:
[tex]r\text{ = (}\frac{1}{t})(\frac{A}{P}-1)[/tex]now, solving we get:
[tex]r\text{ = (}\frac{1}{7})(\frac{1400}{1200}-1)=\text{ }0.02380952[/tex]if we convert this amount into a percentage we get the final answer:
[tex]0.02380952\text{ x 100\% = }2.381[/tex]then, the correct answer is:
2.381% per year
Two girls 21 miles apart. One going 3.5 mph one going 2.5 mph. How long until they meet up?
From the picture,
x + y = 21
From definition,
speed = distance/time
The girl whose speed is 3.5 mph, walks x miles in t hours, that is:
3.5 = x/t
or
x = 3.5t
Similarly,
y = 2.5t
(they walk for the same time)
Replacing into the first equation:
3.5t + 2.5t = 21
6t = 21
t = 21/6
t = 3.5
It will take 3.5 hours until they meet up
A person can join The Fitness Center for $50. A member can rent the tennis ball machine for $10 an hour. Write a linear function to model the relationship between the number of hours the machine is rented (x) and the total cost (y).
Answer: y=10x+50
Step-by-step explanation:
Find the next three terms of the arithmetic sequence. 3/5, 7/10, 4/5,...
Answer:
[tex]\frac{9}{10},1\text{ and 1}\frac{1}{10}[/tex]Explanation:
Given the arithmetic sequence
[tex]\frac{3}{5},\frac{7}{10},\frac{4}{5}\text{.}\cdots[/tex]We can rewrite all the fractions using a denominator of 10 as follows:
[tex]\begin{gathered} \frac{3\times2}{5\times2},\frac{7}{10},\frac{4\times2}{5\times2},\cdots \\ =\frac{6}{10},\frac{7}{10},\frac{8}{10},\cdots \end{gathered}[/tex]We observe that the denominator remains the same but the numerator increases by 1.
Therefore, the next three terms of the arithmetic sequence are:
[tex]\begin{gathered} \frac{9}{10},\frac{10}{10}\text{ and }\frac{11}{10} \\ =\frac{9}{10},1\text{ and 1}\frac{1}{10} \end{gathered}[/tex]