Question 5 (1 point)A student takes a multiple-choice test with 8 questions on it, each of which have 4 choices. The student randomlyguesses an answer to each question.What is the probability that the student gets exactly 4 questions correct?Round to 3 decimal places.a0.886b0.9730.0870.208d
Answers
We can use Binomial distribution to calculate the probability of exactly 4 success
There are 8 questions which is our trial
Probability of succes (p)
Since in every question, there is 4 options with one right answer, then probability of success (p) = 1/4 = 0.25
probabiliti of failure (q) = 1- p = 1- 0.25 = 0.75
We will now use the formula below
[tex]p(x)^{}=^nC_xP^xq^{n-x}[/tex]substitute the values into the formula
[tex]p(x=4)=^{8\text{ }}C_4(0.25)^4(0.75)^{8-4}[/tex][tex]=\frac{8!}{(8-4)!4!}.(0.25)^4.(0.75)^4[/tex][tex]=\frac{8!}{4!4!}\text{.}(0.25)^4(0.75)^4[/tex][tex]=\frac{8\times7\times6\times5\times4!}{4\times3\times2\times1\times4!}\times(0.25)^4\times(0.75)^4[/tex][tex]=\frac{1680}{24}\times(0.00390625)\times(0.31640625)[/tex][tex]\approx0.087[/tex]Related Questions
10 Which number line represents the solution to the inequality -7x - 13 2 8?A-10-5НЕН1005B-10-50510с-10-50510D-10-50510оооо
Answers
The correct option is option A
Explanation:
First we solve the inequality:
-7x -13 ≥ 8
collect like terms:
-7x ≥ 8 + 13
-7x ≥ 21
Divide through by -7:
x ≤ 21/-7
Note: when you divde an inequality by negative number, the iequality sign changes.
x ≤ -3
Since x is less than or equal to -3, the number line starts at -3 and moves towards the left of the number line.
The correct option is option A
Valeria is ordering medals for her school's track meet. Company A charges $4.50 for each medal and a one-time engraving fee of$40. Company B charges $6.50 for each medal and a one-time engraving fee of $20. Which inequality can be used to find x, theleast number of medals that can be ordered so that the total charge for Company A is less than the total charge for Company B?esA)4.5+ 40x<6.5 + 20xB)4.5+ 40x > 6.5 + 20xo4.5x + 40 < 6.5x + 20D)4.5x + 40 > 6.5x + 20
Answers
We will determine the inequality as follows:
*First: We will determine the interception point of the two equations, that is:
[tex]y=4.50x+40[/tex][tex]y=6.50x+20[/tex]So:
[tex]4.50x+40=6.50x+20\Rightarrow4.50x-6.50x=20-40[/tex][tex]\Rightarrow-2x=-20\Rightarrow x=10[/tex]Now, we replace x = 10 on any of the two equations:
[tex]y=4.50x+40\Rightarrow y=4.50(10)+40[/tex][tex]\Rightarrow y=45+40\Rightarrow y=85[/tex]So, the interception point is located at (10, 85).
*Second: We determine the inequality that represents the problem, that is:
[tex]6.50x+20>4.50x+40[/tex][This is overall, the second equation represents greater cost].
*Third: The least number of medals that cab ve ordered so company's A cost is less than company's B cost is 10 medals.
Can I just have a very quick simple answer to this question?
Answers
We have a feasibility region and we have to find at which point of the region the function P can be maximized:
[tex]P=3x+2y[/tex]As this is a linear function, the maximum value will be in one of the vertices of the region. We can identify the vertices as:
We can calculate the value of P for each of the vertices and see which one has a maximum value. We can already guess that P(8,0) will be greater than P(0,8) as the coefficient for x is greater than the coefficient for y.
We can calculate the three values as:
[tex]\begin{gathered} P(0,8)=3\cdot0+2\cdot8=0+16=16 \\ P(6,5)=3\cdot6+2\cdot5=18+10=28\longrightarrow\text{Maximum} \\ P(8,0)=3\cdot8+2\cdot0=24+0=24 \end{gathered}[/tex]Answer: the maximum value of P is 28.
How do you solve 3/4x-9=27
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Solve;
[tex]\begin{gathered} \frac{3}{4}x-9=27 \\ \text{Add 9 to both sides and you now have;} \\ \frac{3}{4}x-9+9=27+9 \\ \frac{3}{4}x=36 \\ Cross\text{ multiply and you now have;} \\ x=\frac{36\times4}{3} \\ x=48 \end{gathered}[/tex]The solution is x = 48
Graph the equation after rewriting it in slope-intercept form. Y-3x=4
Answers
We have this equation
[tex]y-3x=4[/tex]The following is the slope intercept form
[tex]y=mx+b[/tex]add 3x on both sides of the equation
[tex]y-3x+3x=4+3x[/tex]simplify
[tex]y=4+3x[/tex]rearrange
[tex]y=3x+4[/tex]So, the above is the equation in slope-intercept form
Now, let's graph the equation
since this is a linear equation, we need to find 2 points and plot them in the chart
let's find point 1. Let's say x = 0 and replace: y = 3x+4 = 3*0 + 4 = 0 + 4 = 4
so, when x=0, then y = 4 , so our 1st point is (0,4)
now, let's suppose, y=0 , in that case, y = 3x + 4 = 0 , then 3x = -4 , so the value of x is -4/3 = -1.3333
in that case, our seconds point is (-4/3 , 0)
just to make sure, we can also plot a 3rd point, let's say we make x = 2, then y = 3*2 + 4 = 6 + 4 = 10
so, our 3rd point is (2, 10)
using the points above, we can plot something like this...
At a parking garage in a large city, the charge for parking consists of a flat fee of $1.00 plus 1.60 /hr.(a) Write a linear function to model the cost for parking for hours.(Pt)(b) Evaluate P(1.4 )and interpret the meaning in the context of this problem.please make this right I keep making it wrong
Answers
Given:
The charge for parking consists of a flat fee of $1.00 and $1.60 per hour.
To find:
a) Write a linear function P(t).
b) Evaluate P(1.4)
Explanation:
a)
Since the flat fee is $1.00 and the varying fee is $1.60 per hour.
So, the linear function of the total cost for parking is,
[tex]P(t)=1.00+1.60t[/tex]Where t be the number of hours.
b)
Substituting t = 1.4 in the above function we get,
[tex]\begin{gathered} P(1.4)=1.00+1.60(1.4) \\ =1+2.24 \\ P(1.4)=\text{ \$}3.24 \end{gathered}[/tex]That means,
The total cost for parking for 1.4 hours is $3.24.
Final answer:
a) The linear function is,
[tex]P(t)=1.00+1.60t[/tex]b) The value is,
[tex]P(1.4)=3.24[/tex]Estimate 15 5/7- 8 2/7
Answers
Any math tutors available to help me ? I need help
Answers
Hello!
First of all, let's write the initial temperature:
• 6am: 58ºF
In next 5 hours, the temperature rose 1ºF per hour, so:
• 7am: 59ºF
,• 8am: 60ºF
,• 9am: 61ºF
,• 10am: 62ºF
,• 11am: 63ºF
In the next 3 hours, it rose 3ºF per hour:
• 12pm: 66ºF
,• 1pm: 69ºF
,• 2pm: 72ºF
The temperature stayed steady until 6pm:
• In this part, we'll have a constant line until 6pm (it will be 72ºF in all).
In the next 4 hours, the temperature dropped 2ºF per hour:
• 7pm: 70ºF
,• 8pm: 68ºF
,• 9pm: 66ºF
,• 10pm: 64ºF
Dropped steadily until 63ºF at midnight
• 12am: 63ºF
Now, let's make the graph!
State the rule of the perfect squares given the sequence shown below that starts with n = 1 1, 4, 9, 16, 26...
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Given:
the sequence shown below that starts with n = 1
[tex]1,4,9,16,25,\ldots[/tex]The rule of the sequence will be as follows"
The first term = 1, when n = 1
The second term = 4 = 2², when n = 2
The third term = 9 = 3², when n = 3
..
..
So, the rule will be:
[tex]a_n=n^2[/tex]4. Which is the best first step to write 2(x-4)^2-3=8 in standard form?A. Factor.B. Clear the parentheses.C. Set the function equal to 0.D. Combine like terms.
Answers
We will have that the best way to write it in standard form is B, we clear the parentheses and solve for x.
*That is because the function is already factored, and we will combine like terms and equal to 0 in the remaining steps.
NO LINKS!! Show that the triangle with vertices A, B, and C is a right triangle.
Answers
Answer:
[tex][d(A, B)]^2=\boxed{85}[/tex]
[tex][d(A,C)]^2+[d(B,C)]^2=\boxed{85}[/tex]
[tex]\sf Area=\boxed{17}\; units^2[/tex]
Step-by-step explanation:
From inspection of the given diagram, the vertices of the triangle are:
A = (-5, 5)B = (1, -2)C = (-1, 6)If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side. This is the definition of Pythagoras Theorem.
Use the distance formula to find the side lengths of the triangle.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-5))^2+(-2-5)^2}\\&=\sqrt{(6)^2+(-7)^2}\\&=\sqrt{36+49}\\&=\sqrt{85}\end{aligned}[/tex]
[tex]\begin{aligned}d[(A, C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-1-(-5))^2+(6-5)^2}\\&=\sqrt{(-4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\end{aligned}[/tex]
[tex]\begin{aligned}d[(B, C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-1-1)^2+(6-(-2))^2}\\&=\sqrt{(-2)^2+(8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\end{aligned}[/tex]
Therefore:
The longest side of the triangle is line segment AB.The two shorter sides of the triangle are line segments AC and BC.[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
The triangle is a right triangle if:
[tex][d(A,C)]^2+[d(B,C)]^2=[d(A,B)]^2[/tex]
Substitute the found side lengths into the formula:
[tex]\implies [\sqrt{17}]^2+[\sqrt{68}]^2=[\sqrt{85}]^2[/tex]
[tex]\implies 17+68=85[/tex]
[tex]\implies 85=85[/tex]
Therefore, this proves that ΔABC is a right triangle.
To find the area of a right triangle, half the product of the two shorter sides:
[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,C)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{17} \cdot \sqrt{68}\\&=\dfrac{1}{2} \cdot \sqrt{17 \cdot 68}\\&=\dfrac{1}{2} \cdot \sqrt{1156}\\&=\dfrac{1}{2} \cdot \sqrt{34^2}\\&=\dfrac{1}{2} \cdot 34\\&=17 \sf \; units^2\end{aligned}[/tex]
Therefore, the area of the given triangle is 17 units².
George was painting a picture frame. The frame was 5inches wide & 3inches tall. What is the perimeter of the picture frame?
Answers
The perimeter can be calculated by adding the legnths off all 4 sides.
Since it is 5 inches wide and 3 inches tall, it has 2 sides of 5 inches and 2 sides of 3 inches. So, the perimeter is:
[tex]P=5+5+3+3=16[/tex]16 inches.
finally surface area of the solid. use 3.14 for π. write your answer as a decimal.
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To find the total surface area of this cone, we have that the total lateral area is given by the formula:
[tex]A_{\text{lateral}}=s\cdot\pi\cdot r[/tex]Where
s is the slant height of the cone, s = 12 inches.
r is the radius of the base of the cone, r = 7 inches.
To that area, we need to add the area of the base of the cone:
[tex]A_{\text{base}}=\pi\cdot r^2[/tex]That is, this is the area of a circle with this radius. Then, the total surface area is:
[tex]A_{\text{total}=}s\cdot\pi\cdot r+\pi\cdot r^2[/tex]Substituting the values in this formula, we have:
[tex]A_{\text{total}}=12in\cdot3.14\cdot7in+\pi\cdot(7in)^2=263.76in^2_{}+153.86in^2[/tex]Then
[tex]A_{\text{total}}=417.62in^2[/tex]Hence, the total area is equal to 417.62 square inches.
How should you solve the equation x + 10 = 80? What is the resulting equivalent equation?Choose the correct answer below.
Answers
Multiply each side by 10, then simplify
Here, we want to know how to proceed with solving the equation
As we can see, we have the division sign between the terms on the left hand side of the equation
To solve the equation, we have to find the value for x by isolating it
What this mean here is that we will have to multiply both sides by 10; so that we can isolate x
Thus, the correct answer here is to multiply each side by 10, then simplify
cole is studying ceramics and he was asked to submit 5 vessels from his collection to exhibit at the fair. he has 15. vessels that he thinks are show worthy. in how many ways can the vessels be chosen
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Since he has 15 vessels and needs to choose 5, we can use a combination of 15 choose 5 to calculate the number of possible ways, since the order of the vessels inside the group of 5 is not important.
The formula to calculate a combination of n choose p is:
[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]Then, for n = 15 and p = 5, we have:
[tex]\begin{gathered} C(15,5)=\frac{15!}{5!(15-5)!}=\frac{15!}{5!10!}=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10!}{5\cdot4\cdot3\cdot2\cdot10!} \\ =\frac{15\cdot14\cdot13\cdot12\cdot11}{5\cdot4\cdot3\cdot2}=3003 \end{gathered}[/tex]So there are 3003 ways to choose the 5 vessels.
Jacob is taking part in a month long Reading challenge at his school. He can earn point for each book he reads, up to two dozen books. As shown in the graph P (b) gives the number of points Jacob earns as a function of the number of books he reads.
Answers
Observe the given graph carefully.
It is evident that 'b' is the independent variable (representing the number of books read) for the function f(b) (representing the number of points earned).
The domain of a function is the set of all values of the independent variable that lie within the function.
The graph is plotted from x=0 to x=24.
And the number of books cannot be fractional.
So it can be concluded that the domain of the function is the set of whole numbers from 0 to 24. Also, the function is also defined at the end-points. So the set will be inclusive of the end-points 0 and 24.
Therefore, the 2nd option is correct for the first blank.
The domain is a subset of all possible values of variable 'b'. So it will represent the number of books that Jacob reads.
Thus, the 1st option is the correct choice for the second blank.
Hello for this particular problem can I change the final results to a whole number? or it is not possible?
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We are asked which of the given combinations will produce a number that is less or equal to 25.
For A we have:
[tex]A=3(8\frac{3}{4})[/tex]Let's remember that for a mixed fraction we have:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]Therefore, we can change the mixed fraction and we get:
[tex]A=3(8\frac{3}{4})=3(8+\frac{3}{4})[/tex]Solving the operations:
[tex]A=26.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For B we have:
[tex]B=2(10\frac{1}{4})[/tex]Changing the mixed fraction:
[tex]B=2(10\frac{1}{4})=2(10+\frac{1}{4})[/tex]To solve the operation we will apply the distributive property:
[tex]B=20+2\times\frac{1}{4}[/tex]Now, we simplify the fraction:
[tex]B=20+2\times\frac{1}{4}=20+\frac{1}{2}[/tex]Now, we use the fact that 1/2 = 0.5:
[tex]B=20+\frac{1}{2}=20+0.5=20.5[/tex]Since we get a number that is less than 25 this is a train he can ride.
For C we have:
[tex]C=2(7\frac{1}{2})+10\frac{1}{4}[/tex]Changing the mixed fraction:
[tex]C=2(7+\frac{1}{2})+10+\frac{1}{4}[/tex]Now, we apply the distributive property:
[tex]C=14+1+10+\frac{1}{4}[/tex]Solving the operations. We use the fact that 1/4 = 0.25:
[tex]C=25+0.25=25.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For D.
[tex]D=7\frac{1}{2}+2(8\frac{3}{4})[/tex]Now, we change the mixed fractions:
[tex]D=7+\frac{1}{2}+2(8+\frac{3}{4})[/tex]Now, we use the distributive property:
[tex]D=7+\frac{1}{2}+16+2\times\frac{3}{4}[/tex]Simplifying the fraction:
[tex]D=7+\frac{1}{2}+16+\frac{3}{2}[/tex]Now, we add the fractions, we have into account that when fractions have the same denominator we can add the numerators and use the common denominator, like this:
[tex]D=7+\frac{4}{2}+16[/tex]Simplifying the fraction we get:
[tex]D=7+2+16[/tex]Solving the operations:
[tex]D=25[/tex]Since we get 25 this is a trail that he can ride.
can you help me with my work
Answers
Conn Math increase by 3 , each week
Conn Sci increase doubling number, every week
Then now fill table
. Week. 1. Conn Math. Conn Sci
. Week 1. 25. 25
. Week 2. 28. 50
. Week 3. 31. 75
. Week 4. 34. 100
Now part. B
A linear model is when data fits in a straight line
hence Then
Then
First model of Conn Math is
Visitors. = 25 + 3 W
Second model for Conn Sci
Visitors = 25 x
Wally's grandmother started a college savings account for him with $3,000. What is the total amount of money in the account after 5 years if the annual simple interest rate is 3%?
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ANSWER
$3,450
EXPLANATION
She started the savings account with $3,000.
The simple interest rate is 3% and the number of years is 5 years.
To find the amount of money in the account after 5 years, we have to first find the interest and then add it to the initial amount saved.
Simple Interest on an amount of money (Principal) at a rate R for a number of years T is given as:
[tex]I\text{ = }\frac{\text{P }\cdot\text{ R }\cdot\text{ T}}{100}[/tex]Therefore, the interest is:
[tex]\begin{gathered} I\text{ = }\frac{3000\cdot\text{ 5 }\cdot\text{ 3}}{100} \\ I\text{ = \$450} \end{gathered}[/tex]Therefore, the amount in the account after 5 years is:
Amount = Principal + Interest
Amount = 3000 + 450
Amoun = $3,450
That is the amount in the account.
Brian glues together 4 wooden cubes as shown. Each cube has an edge of 5 centimeters. He covers the surface area of this new figure with metallic paper that is cut to size for each face.A. 125 square cm B. 150 square cm C. 450 square cm D. 600 square cm
Answers
Explanation:
The new figure is a square prism, with the sides that measure 4x5 = 20 cm.
We have to find the surface area of this prism. To do this we have to find the area of the rectangular faces and the area of the base, which is the same as the area of the top. The total surface area is 4 times the area of the rectangular face plus 2 times the area of the base/top.
[tex]A_{\text{rectangular face}}=20\operatorname{cm}\times5\operatorname{cm}=100\operatorname{cm}^2[/tex][tex]A_{\text{base}}=5\operatorname{cm}\times5\operatorname{cm}=25\operatorname{cm}^2[/tex][tex]\begin{gathered} S=4\cdot A_{\text{rectangular face}}+2\cdot A_{base} \\ S=4\cdot100\operatorname{cm}+2\cdot25\operatorname{cm}^2 \\ S=400\operatorname{cm}+50\operatorname{cm}^2 \\ S=450\operatorname{cm}^2 \end{gathered}[/tex]Answer:
C. 450 cm²
Explain why the two right triangles are not the same.
Answers
Step 1:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
Step 2:
Write the corresponding sides and angles
The angles are not corresponding to the sides
Step 3
[tex]\begin{gathered} \angle T\text{ }\ne\text{ }\angle E \\ \angle S\text{ }\ne\text{ }\angle D \\ \angle R\text{ }\ne\angle F \end{gathered}[/tex]Final answer
The two right angles are not the same because the sides and the angles are not corresponding.
The options are A,B,C,D can we make this quick please I am in a rush to turn this in!! thank you so much.
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The function we have is:
[tex]y=-x+4[/tex]First, we need to find the rate of change of this function and then we can compare it with the rate of change of each option.
To find the rate of change, we compare the given equation with the general slope-intercept equation:
[tex]y=mx+b[/tex]Where m is the slope, also called the rate of change and b is the y-intercept.
By comparing the two equations, we find that the rate of change is:
[tex]m=-1[/tex]So now we will analyze the given options to see in which of them we find a rate of change of -1.
Option A:
In this option (and in option B) we have a table of values for x and y.
We calculate the rate of change by taking two (x,y) points from the table,
Here, we will take the first two (x,y) values and label them as follows:
[tex]\begin{gathered} x_1=-4 \\ y_1=1 \\ x_2=-2 \\ y_2=2 \end{gathered}[/tex]And we calculate the rate of change "m" using the slope formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Substituting the values we get:
[tex]m=\frac{2-1}{-2-(-4)}[/tex]Solving the operations:
[tex]\begin{gathered} m=\frac{1}{-2+4} \\ m=-\frac{1}{2} \end{gathered}[/tex]The rate of change if NOT -1, this option is not correct.
Option B. We do the same as in the first option.
Label the first two (x,y) values as follows:
[tex]\begin{gathered} x_1=4 \\ y_1=5 \\ x_2=8 \\ y_2=8 \end{gathered}[/tex]And use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values:
[tex]\begin{gathered} m=\frac{8-5}{8-4} \\ m=\frac{3}{4} \end{gathered}[/tex]Again, the slope or rate of change is NOT -1, this is also not the option we are looking for,
Option C. In options, C and D we have a graph. To find the rate of change from the graph of a line, we take two points where the line passes, and find the rate of change as follows:
[tex]m=\frac{\text{change in y}}{change\text{ in x}}[/tex]For the graph in C, we will take the following red points
Drawing a triangle between the points we can find the change in y and the change in x:
[tex]\begin{gathered} \text{change in y=-1} \\ \text{change in x=1} \end{gathered}[/tex]Thus, the rate of change is:
[tex]\begin{gathered} m=-\frac{1}{1} \\ m=-1 \end{gathered}[/tex]C is the correct option.
A model of a triangular prism is shown below. Whats is the surface area of the prism?
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We are asked to find the surface area of a triangular prism. To do that we must add the areas of each of the faces of the prism, that is, three rectangles and two triangles. The area of each rectangle is:
[tex]A_{\text{rectangles }}=5\operatorname{cm}\times12\operatorname{cm}+5\operatorname{cm}\times12\operatorname{cm}+5\operatorname{cm}\times12\operatorname{cm}[/tex]Solving the operations we get:
[tex]A_{\text{rectangles}}=180cm^2[/tex]Now we find the area of the triangles, knowing that the area of a triangle is the product of its base by its height over two, like this:
[tex]A_{\text{triangle}}=\frac{(base)(height)}{2}[/tex]The base is 5 cm and the height is 6cm, replacing we get:
[tex]A_{\text{triangle}}=\frac{(5\operatorname{cm})(6\operatorname{cm})}{2}=15cm^2[/tex]Now we add both areas having into account that there are two triangles, like this:
[tex]A=A_{\text{rectangle}}+2A_{\text{triangle}}[/tex]Replacing we get:
[tex]\begin{gathered} A=180+2(15) \\ A=210 \end{gathered}[/tex]therefore, the surface area is 210 square centimeters
HELP graph the solution of system of linear inequality's
y< - 5x - 3
y>x+5
Answers
The graph of solution of system of linear inequality can be obtained by plotting the given equations and and then shading the region according to the inequality sign.
How to graph two linear inequality?
To graph Linear equations with inequality consider the equations as linear equation in two variable.Obtain two points for each line which satisfies the equations and plot them on graph. For example (1,6) and (-1,4) satisfies the equation y=x+5.Now shade the region according to the inequality: < : below the line> : above the lineHence you obtain the graph for the solution of system of the given linear equation with inequality.Any point in this region will satisfy both the linear inequalities (check the graph attached below).To know more about linear inequality visit
https://brainly.com/question/11897796
#SPJ1
Solve 8sin(pi/6 x) = 4 for the four smallest positive solutions
Answers
Simplify the given expression as shown below
[tex]\begin{gathered} 8sin(\frac{\pi}{6}x)=4 \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{4}{8}=\frac{1}{2} \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{1}{2} \end{gathered}[/tex]On the other hand,
[tex]\begin{gathered} sin(y)=\frac{1}{2} \\ \end{gathered}[/tex]Solving for y using the special triangle shown below
Thus,
[tex]\begin{gathered} \Rightarrow y=30\degree\pm360\degree n=\frac{\pi}{6}\pm2\pi n \\ and \\ y=150\degree+360\degree n=\frac{5\pi}{6}+2\pi n \end{gathered}[/tex]Then,
[tex]\begin{gathered} \Rightarrow\frac{\pi}{6}x=y \\ \Rightarrow\frac{\pi}{6}x=\frac{\pi}{6}+2\pi n \\ \Rightarrow x=1+12n \\ and \\ \frac{\pi}{6}x=\frac{5\pi}{6}+2\pi n \\ \Rightarrow x=5+12n \end{gathered}[/tex]The two sets of solutions are
[tex]x=1+12n,5+12n[/tex]Then, the four smallest positive solutions are[tex]\Rightarrow x=1,5,13,17[/tex]The answers are 1,5,13,17what is the whole number equal to 1000 / 4
Answers
In this case, the answer is very simple.
We must perform the division and verify that the result is a whole number.
1000 / 4 = 250 ===> 250 is a whole number
The answer is:
The number is 250 .
Answer:
250, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
if you simply devide 1000 by 4 then you get 250 wich yes , is indeed a whole number ^^
Based on the graph, find the range of y = f(x).[0,^3sqrt13 ][0, 8][0, ∞)[0, 8)
Answers
Given the function:
[tex]f(x)=\begin{cases}4;-5\le x<-2 \\ |x|;-2\le x<8 \\ ^3\sqrt[]{x};8\le x<13\end{cases}[/tex]The graph of the function is as shown in the figure:
The range of the function will be as follows:
The minimum value of y = 0
And the maximum value of y = 8 (open circle)
So, the range of the function = [0, 8)
6Question(15 Points)6. The volume of the cylinder below is 150 cubic centimeters. What is the area of its base?a. 20 cmb. 20 cmc. 10 cmd. 10 cm7.5 cm
Answers
The given cylinder has a height of 7.5 cm and volume of 150 cubic centimeters,
[tex]\begin{gathered} h=7.5\text{ cm} \\ V=150\text{ cm}^3 \end{gathered}[/tex]Consider that the volume and base area of a right circular cylinder are related as,
[tex]V=A\times h[/tex]Substitute the values and solve for A,
[tex]\begin{gathered} 150=A\times7.5 \\ A=\frac{150}{7.5} \\ A=20 \end{gathered}[/tex]Thus, the base area of the given cylinder is 20 sq. cm.
Therefore, option b is the correct choice.
I need help. I think I left out a step. I need to find the volume of the rectangle prism.
Answers
Given a rectangular prism with the following dimensions:
H = Height = 26
L = Length = 20
W = Width = 12
To be able to determine its volume, we will be using the following formula:
[tex]\text{ Volume = L x W x H}[/tex]We get,
[tex]\text{ Volume = L x W x H}[/tex][tex]\text{ = 20 x 12 x 26}[/tex][tex]\text{ Volume = }6240[/tex]Therefore, the volume of the rectangular prism is 6,240.
Draw the reflection of the figure in the x-axis. Polygon + Move - Redo 5 4 3 2 1 4 -3 -2 -29 1 5
Answers
Answer
Explanation
To draw the image of this figure, we need to first obtain the coordinates of the edge of the image of this figure.
And to do that, we need to first write the coordinates of the edges of the original figure.
When a given coordinate A (x, y) is reflected across the x-axis, the coordinates become A' (x, -y).
The coordinates of the original image include (-2, -4), (1, -3) and (3, -4)
After the reflection, we will now have
(2