The least multiple of a number is itself.
Least multiple of 8 : 8
What is the exact value of tan 7pi/12? Thank you!
Remember that
[tex]tan(\frac{7\pi}{12})=tan(105^o)=-tan(75^o)=-tan(45^o+30^o)[/tex]and
[tex]tan(A+B)=\frac{tanA+tanB}{1-tanA*tanB}[/tex]therefore
[tex]tan(45^o+30^o)=\frac{tan45^o+tan30^o}{1-tan45^o*tan30^o}[/tex]substitute given values
[tex]tan(45^o+30^o)=\frac{1+\frac{\sqrt{3}}{3}}{1-(1)(\frac{\sqrt{3}}{3})}=\frac{\frac{3+\sqrt{3}}{3}}{\frac{3-\sqrt{3}}{3}}=\frac{3+\sqrt{3}}{3-\sqrt{3}}*\frac{3+\sqrt{3}}{3+\sqrt{3}}=\frac{9+6\sqrt{3}+3}{6}=\frac{12+6\sqrt{3}}{6}=2+\sqrt{3}[/tex]therefore
The answer is
[tex]tan(\frac{7\pi}{12})=-(2+\sqrt{3})[/tex]The answer is the second option
66 randomly selected students were asked the number of pairs of shoes they have. Let X representthe number of pairs of shoes. The results are as follows:# of Pairs of Shoes 4Frequency 75 68 9 10 114 11 11 11 2 12 8Round all your answers to 4 decimal places where possible.The mean is:The median is:The sample standard deviation is:The first quartile is:The third quartile is:What percent of the respondents have at least 10 pairs of shoes?9617% of all respondents have fewer than how many pairs of shoes?
Given data
1. The mean
[tex]\frac{\sum fx}{\sum f}=\frac{505}{66}=7.6515[/tex]2. The median
[tex]\begin{gathered} \text{ Median = (}\frac{\text{N+1}}{2})th \\ =(\frac{66+1}{2})th=(\frac{67}{2})th=33.5th \\ \text{The median is the 33.5th }term\text{ which is between 7 and 8} \\ \text{The median is }\frac{\text{7+8}}{2}=\frac{15}{2}=7.5 \end{gathered}[/tex]3. The sample standard deviation
[tex]\begin{gathered} SD\text{ =}\sqrt[]{\frac{\sum f|x-\bar{x}|}{\sum f}} \\ \bar{x}=7.6515 \\ SD=\sqrt[]{4.8028} \\ SD=2.1915 \end{gathered}[/tex]Estimate the point(s) at which the graph of f has a local maximum or a local minimum.
The graph of f has a local maximum of coordinates at (-2.5, 30) and a local minimum of coordinates at (2.5, -30)
What are Maxima and Minima of a Function?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
As per the given graph,
From the given graph it is noticed that the highest point of the function is (-2.5, 30), therefore the local maxima is (-2.5, 30).
From the given graph it is noticed that the lowest point of the function is (2.5, -30), therefore the local maxima is (2.5, -30).
The graph of f has a local maximum of coordinates at (-2.5, 30)
The graph of f has a local minimum of coordinates at (2.5, -30)
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Solve for the given variables
Answer:
7.5?
Step-by-step explanation:
I'm not sure but i think 60=8x so you would do 60÷8 and it's 7.5
Geri encarga arreglos florales para un almuerzo de agradecimiento para un maestro.Planea comprar hasta ocho arreglos de mesa que cuestan $5 cada una,con una tarifa de $10 por todo el pedido.Representa gráficamente la función para el precio.
From the graph drawn above, we can see the relationship between the flower arrangements and the cost of ordering each of them.
On the x axis you have the number of orders,and on the y axis you have the cost of each order. Each flower arrangement costs $5, and the cost of fare is $10. That means the cost for each order would shown as follows;
1 order = 5 + 10 (15)
2 orders = 10 + 10 (20)
3 orders = 15 + 10 (25)
4 orders = 20 + 10 (30)
5 orders = 25 + 10 (35)
6 orders = 30 + 10 (40)
7 orders = 35 + 10 (45)
8 orders = 40 + 10 (50)
Therefore, the ordered pair for this graph is as follows;
(1, 15), (2, 20), (3, 25), (4, 30), (5, 35), (6, 40), (7, 45), (8, 50)
That is, when x = 1, y = 15, when x = 2, y = 20..., and so on.
Find the maximum value of the function z = 4x+2y subject to the following constraints.
x≥5
y≥4
4x+3y≤56
The function at its maximum value will be at point (11,4) and its value is 52 which can be derived keeping in mind the constraints that have been given.
Maximizing a functionThe maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.
There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.
Herein we can find the closed region ABC from the three equations or constraints given
and can mark the points as
A = (5,4)
B = (5, 12)
C = (11, 4)
if we put up the values of the points, we get
at (11, 4), Z = 4 x 11 + 2 x 4
=52 that is the maximum value amongst the three.
Thus, the maximum point of the function can be calculated as (11,4)
How do you extract out the maximum or minimum value of a function?We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.
If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value
What is the maximum value of a function called?The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.
There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum
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jeriel leans a 26 foot ladder against a wall so that it forms an angle of 61 with the ground .
To solve this problem we will use the following diagram:
where d is the distance between the base of the ladder and the wall.
Using the cosine we get:
[tex]\cos 61^{\circ}=\frac{d}{26ft}.[/tex]Multiplying the above equation by 26ft we get:
[tex]\begin{gathered} \cos 61^{\circ}\times26ft=\frac{d}{26ft}\times26ft\text{.} \\ d=26ft\cdot\cos 61^{\circ}\text{.} \end{gathered}[/tex]Then:
[tex]d\approx12.60505013ft\approx12.61ft.[/tex]Answer: 12.61.
If the paint costs $1.50 per square meter, how much will she spend to cover the entire wall with paint?
To find the price to paint the entire wall, we just need to find the area of the wall and multiply by the price per square meter.
The area of a square is given by the product of the side length by itself. Since the measure of the side is 3 meters, the area is
[tex]A=3^2=9[/tex]9 m².
The unitary price per square meter is $1.50. Multiplying this value by the area, we have
[tex]9\times1.5=13.5[/tex]It will cost $13.50 to paint the wall.
In the diagram below, AB || DEF, AE and BD intersect at C, m2B = 43°, and mZCEF = 152°.
From the picture, we have the necessary information:
The supplementary angles.
The parallels being intersected by two secant lines. And alternate interior angles are congruent under this condition.
The other angle of the triangle is then:
As a result, the angles vertical angles, therefore
< BAC = 28 (it confirms the alternate interior angle Therefore, we can write all the angles in the following drawing:
ersion with whole number valuesA flower bed has the shape of a rectangle 8 yards long and 3 yards wide. What is its area in square feet?Be sure to include the correct unit in your answer.ft
Given that length =8 yards and width = 3 yards of the rectangle bed.
Recall the formula for the area of the rectangle is
[tex]A=\text{length }\times width[/tex][tex]\text{Substitute length =8 yards and width=3 yards, we get}[/tex][tex]A=8\text{ yards }\times3\text{ yards}[/tex][tex]A=8\times3yards^2[/tex][tex]A=24yards^2[/tex]We know that one yard=3 feet.
[tex]\text{yards}^2=(3\text{ f}eet)^2[/tex][tex]\text{yards}^2=\text{ 9 f}eet^2[/tex][tex]\text{Substitute }yards^2=9\text{ f}eet^2\text{ in the area of the rectangle as follows.}[/tex][tex]A=24\times9\text{ fe}et^2[/tex][tex]A=216\text{ fe}et^2[/tex]Hence the area of the rectangle flower bed is 216 square feet.
Use the net to find the surface area of the prism. 5 ITL 13 m 5 IT 13 m 12 m 29 m 12 m 13 YTL 5 ICE 29 YTL 5 YC Not drawn to scale 930 m2 o 11,310 m2 0 45,240 m2 118 m2
To find the surface area of the prism, we will consider the areas of each part of the net
For part A
Area of A = L x B = 29 x 5 = 145
Area of B = L X B = 29 x 13 = 377
Area of C = L x B = 29 x 12 =348
Area of D = 1/2 x H X B = 1/2 x 12 x 5 = 30
Area of E = 1/2 x H x B = 1/2 x 12 x 5 = 30
Total Area = 145 + 377 + 348 + 30 + 30
Answer the questions below.
(a) Daily high temperature
The daily high temperature does not depend on the number of ticket sales.(b) Amount of sleep
The amount of medication influences the amount of sleep.(c) Input U
The independent variable is the input.PLease tell me if its linear exponential quadratic please
Answer:
Linear
Step-by-step explanation:
X values are increasing equally by 1. Y values are decreasing equally by 2. So, the graph is a linear graph.
If it is 3:40 p.m. in Denver, what time is it in Miami?
Answer:
5:40 P.M.
Explanation:
From the time map:
• When the time in Denver is 10.00 AM
,• The time in Miami is 12:00 Noon
This means that Miami is 2 hours ahead of Denver.
Thus, if it is 3:40 p.m. in Denver:
[tex]\begin{gathered} \text{Time in Miami}=3\colon40+2\colon00 \\ =5\colon40p.m\text{.} \end{gathered}[/tex]It is 5:40 P.M. in Miami.
if y =3x^3 + 2x^2 - 5x + 2, find d^3y/dx^3
Answer:
18
Step-by-step explanation:
[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]
Find 75% of 150. Round to the nearest tenth if necessary.
Find 75% of 150
First, let's convert 75% to decimal by dividing by 100:
[tex]\frac{75}{100}=0.75[/tex]Now, we will multiply 0.75 with 150 to find out answer:
[tex]\begin{gathered} 0.75\times150 \\ =112.5 \end{gathered}[/tex]Answer112.5I believe that it would be 112.5.
__________________________________________
Convert 75% to a decimal by dividing it by 100:
[tex]\frac{75}{100} = 0.75[/tex]
Next, multiply 0.75 to 150:
[tex]0.75[/tex] × [tex]150 = 112.5[/tex] ← Final Solution
Hope this helps!
Three horse share five bales of hay equally. Five cows share eight bales of hay equally.
How much hay does each horse and each cow get?
Which animal gets more, a horse of a cow? How much more hay do they get?
How much hay does each horse and each cow get?
(a)The hay shared by 3 horses = 5 bales
So, the hay shared by 1 horse = x
Rewriting the statements ,
3 h = 5 b --(1)
1 h = x -(2)
By applying cross multiplication method to (1) and (2)
3 (x) = 5
x = 5/3
The hay shared by 1 horse = 5/3
(b)The hay shared by 5 cows = 8 bales
So, the hay shared by 1 cow = y
Rewriting the statements ,
5 c = 8 b --(3)
1 c = y -(4)
By applying cross multiplication method to (3) and (4)
5 (y) = 8
x = 8/5
The hay shared by 1 cow = 8/5
Which animal gets more, a horse of a cow?
Comparing the fractions,
The hay shared by 1 horse = 5/3 = 1.7
The hay shared by 1 cow = 8/5 = 1.6
1.7 > 1.6
So, a horse gets more than a cow
How much more hay do they get?
Considering the difference of fractions,
Amount of more hay consumed = Hay shared by a horse - hay shared by a cow.
[tex]=\frac{5}{3} -\frac{8}{5} \\\\=\frac{25-24}{15} \\\\=\frac{1}{15}[/tex]
The horse share [tex]\frac{1}{15}[/tex] more hay than cows
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Find the equation of a line parallel to the line y = −5/4x + 7. Write the equation in Standard Form (Ax + By = C).
The equation to be found is parallel to
[tex]y=2x+5[/tex]2 lines that are parallel have the same slope. Therefore,
[tex]\begin{gathered} m_1=m_2 \\ m_2=2 \end{gathered}[/tex]The equation to be found is containing the point (3, 3)
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \\ 3=2(3)+b \\ 3-6=b \\ b=-3 \end{gathered}[/tex][tex]y=2x-3[/tex]the base of the triangle prism shown below is a right triangle. What is the lateral surface area of the prism
Given data:
The given triangular prism.
The expression for lateral surface area is,
[tex]\begin{gathered} LS=(8\operatorname{mm}+\text{ 6mm +}10\text{ mm)}\times12\text{ mm} \\ =288\text{ sq-mm} \end{gathered}[/tex]Thus, the lateral surface area is 288 sq-mm.
Which of the following is the correct mathematical expression for:
Halve a number and then increase it by five
Answer:
1/2 x + 5
Step-by-step explanation:
Haf of x = 1/2 x
then add 5 : 1/2 x + 5
In right triangle ABC, CD¯¯¯¯¯ is the altitude to hypotenuse AB¯¯¯¯¯. If AB = 28.3¯ and DB = 12, find CD.
The side of the right triangle CD is 25.63 units
How to find side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
Base on the angles, the side of a right triangle can be named as follows:
opposite sidehypotenuse sideadjacent sideTherefore, the side CD of the right triangle can be found as follows:
using Pythagoras theorem,
c² = a² + b²
Hence,
CD = √28.3² - 12²
CD = √800.89 - 144
CD = √656.89
CD = 25.6298653918
Therefore,
CD = 25.63 units
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Which expression is equivalent to the following complex fraction?SIMI3+3y+5x2(y-2x)2(y-2x)3y-5xo122(y-2x)(3y-5x)x²,2x²y²2(y-2x) (3y-5x
Solution
For this case we can do the following:
[tex]\frac{\frac{2}{x}-\frac{4}{y}}{-\frac{5}{y}+\frac{3}{x}}[/tex]We can start with the numerator and we have:
[tex]\frac{2}{x}-\frac{4}{y}=\frac{2y-4x}{xy}=\frac{2(y-2x)}{xy}[/tex]For the denominator we have:
[tex]-\frac{5}{y}+\frac{3}{x}=\frac{3y-5x}{xy}[/tex]And replacing we got:
[tex]\frac{\frac{2(y-2x)}{xy}}{\frac{3y-5x}{xy}}=\frac{2(y-2x)}{3y-5x}[/tex]Then the correct answer would be:
[tex]\frac{2(y-2x)}{3y-5x}[/tex]Solve for this angle.
X+87° 2x° i have to solve for the angle with the 2 on it
Answer:
x=31
Step-by-step explanation:
x+87+2x=180(angles on a straight line is equal to 180)
3x+87=180
3x=180-87
3x=93
x=31
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each card in a set of cards has a different number of 1 to 12 written on it a student randomly chooses a car record two numbers shown on the card and replaces the card the table shows the results of the students choosing a card 25 x number of Cars 1 2 3 4 5 6 7 8 9 10 11 12 number of outcomes +23-142-311-2213 space on the data in the table how many of the next 125 cars of the student chooses could be expected to have a number shown on a car that is a multiple of 4
Given data:
The given table is shown.
The expression for the probability that the number is multiple of 4.
[tex]\begin{gathered} P(4m)=\frac{8}{25} \\ =0.32 \end{gathered}[/tex]When 125 times the cards are chosen then expected number card is multiple of 4 is,
[tex]\begin{gathered} E(4m)=125\times0.32 \\ =40 \end{gathered}[/tex]Thus, the correct option is (A).
evaluate 7x^2+2(3x-8)-5x for x=3. show your work
The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 will be 50.
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The expression is,
7x² + 2(3x - 8) - 5x
Now, The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 calculated as;
The expression is,
7x² + 2(3x - 8) - 5x
Now, For the value of expression 7x² + 2(3x - 8) - 5x for x = 3 , we can substitute x = 3;
7x² + 2(3x - 8) - 5x
7 (3)² + 2 (3 × 3 - 8) - 5 × 3
7 × 9 + 2 (9 - 8) - 15
7 × 9 + 2 × 1 - 15
63 + 2 - 15
65 - 15
50
So, For x = 3,
⇒ 7x² + 2(3x - 8) - 5x = 50
Thus, The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 will be 50.
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Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 7t+5−−−−−√=7 Enter the exact answers.
The given equation is
[tex]\sqrt[]{7t+5}=7[/tex]Square both sides to cancel the square root
[tex]\begin{gathered} (\sqrt[]{7t+5})^2=(7)^2 \\ 7t+5=49 \end{gathered}[/tex]Subtract 5 from both sides
[tex]\begin{gathered} 7t+5-5=49-5 \\ 7t=44 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7t}{7}=\frac{44}{7} \\ t=\frac{44}{7} \\ t=6\frac{2}{7} \end{gathered}[/tex]The solution is t = 44/7 OR t = 6 2/7 (mixed number)
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ΔMNQ ≅ ΔONP are Congruent triangle.
What do you mean by congruent?
Two figures are considered to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when positioned one on top of the other. Congruent refers to things that are exactly the same size and shape.1) MN = ON ⇒ Given
2) ∠1 = 2 ⇒ Angles are equal because sides are equal.
3) MN = ON,MP = OQ ⇒ Given
4) ΔNMP and ΔNQO are isosceles trisngle.
5) PN = QN ⇒ Given
6) PQ = QP ⇒ Line segment
7) MP + PO = OQ + QM ⇒ Adding = amount to = line segment
8) ΔMNQ ≅ ΔONP = Congruent
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21 out of 24 did their edpuzzle what percent did their edpuzzle?
1) To calculate it, we can set a proportion
24--------100%
21---------x
Cross multiply it
x =2100/24
x=87.5
87.5%
Answer: 87.5% did
Step-by-step explanation:
Match the coordinate rule with the reflection that produces it.Column AColumn B1.Reflect across the x-axisa. (b, a)2.Reflect across the y-axisb. (a, b)3.Reflect across the originC. (-b, -a)4.Reflect across the line y = xd. (-a, -b)5.Reflect across any horizontal line. Ex: y = -2e. (a, -b)f. (2x-a, b)6.Reflect across any vertical line. Ex: x = 5g. (a, 2y-b)
4. Reflect across the line y = x ------- (b,a)
for reflection across the line y=x, the value of x and y coordinates are interchanged;
[tex](x,y)\rightarrow(y,x)[/tex]5. Reflect across any horizontal line. Ex: y = -2 ......... (a,2y-b)
for reflection across any horizontal line, the x coordinate remain the same but the y coordinate is subtracted from twice the value of the y coordinate of the line of reflection.
[tex](x,y)\rightarrow(x,2y_1-y)[/tex]6. Reflect across any vertical line. Ex: x = 5 ---------- (2x-a, b)
for reflection across any vertical line, the y coordinate remain the same but the x coordinate is subtracted from twice the value of the x coordinate of the line of reflection.
[tex](x,y)\rightarrow(2x_1-x,y)[/tex]You invest $940 into an account that
earns 8% simple interest. What is the final
In the account after 6 years
The final amount in the account after 6 years is $6,354.4
This is a problem with simple interest. We can solve this problem by following a few steps.
I have invested $940 into an account that earns 8% simple interest.
We have to use a formula to solve this problem.
I = P× r× t
Where I = amount of interest.P is denoted as the principal amount of money which is $940 as per the question.r is denoted as simple interest which is 8%, according to the question.t represents the period which is 6 years or 72 months as 1 year is equal to 12 months.So, the interest after 6 years is, (940 × 8 × 72) / 100 = $5,414.4
The total amount after 6 years is ( 940+ 5414.4 ) = $6,354.4 [ Total amount = principal amount + interest ]
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