Answer:
03*36 108 the positive number
Coffee Shop PricesCup CostSmall $2Regular $4Large $5David and Jon are placing coffee orders for their friends.David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a $50 bill.Jon wants to know how much he spent on coffee.What is a good plan to find the amount Jon spent on coffee?3rd grade student
Step 1:
Cost of large cup = $5
Step 2:
Number of large David orders = 10 cups
A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.
Jon order 4 fewer large cups
Therefore,
Jon order = 6 cups
Step 3:
A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.
The amount Jon spent on coffee = 6 x $5 = $30
Find the exact value of sin,cos, and tan for the angle while simplifying all roots.
We can solve these values using the next triangle:
First, we need to label the sides using the angle of 30 degrees.
- The largest side is always the hypotenuse, h = 1.
- The opposite side is opposite to the angle, opp = 1/2.
- The adjacent side is between the angle of 30 degrees and the right angle,
adj = √3/2.
Now, we can solve the trigonometric expressions:
For sin:
sin θ = opposite side / hypotenuse
sin 30 = (1/2) / 1
sin 30 = 1/2
For cos:
cos θ = adjacent side / hypotenuse
cos 30 = (√3/2)/1
cos 30 =√3/2
For tan:
tan θ = opposite side / adjacent side
tan 30 =(1/2) / (√3/2)
Simplify the fractions:
tan 30 = 1/√3
Hello, may I have help with finding the maximum or minimum of this quadratic equation? Could I also know the domain and range and the vertex of the equation?
To solve this problem, we will use the following graph as reference:
From the above graph, we get that the quadratic equation represents a vertical parabola that opens downwards with vertex:
[tex](3,5)\text{.}[/tex]The domain of the function consists of all real numbers, and the range consists of all numbers smaller or equal to 5.
Answer:
Maximum of 5, at x=3.
Vertex (3,5).
Domain:
[tex](-\infty,\infty).[/tex]Range:
[tex](-\infty,5\rbrack.[/tex]The slope and y-intercept of the relation represented by the equation 12x-9y+12=0 are:
12x - 9y +12 =0
To find the slope and y intercept, we want to put the equation in slope intercept form
y = mx+b where m is the slope and b is the y intercept
Solve the equation for y
Add 9y to each side
12x - 9y+9y +12 =0+9y
12x+12 = 9y
Divide each side by 9
12x/9 +12/9 = 9y/9
4/3 x + 4/3 = y
Rewriting
y = 4/3x + 4/3
The slope is 4/3 and the y intercept is 4/3
Graph the reflection of the polygon in the given line
Let:
[tex]\begin{gathered} A=(-3,2) \\ B=(1,-1) \\ C=(-2,-2) \\ D=(-4,-1) \end{gathered}[/tex]After the reflection over y = -x:
[tex]\begin{gathered} A->(-y,-x)->A^{\prime}=(-2,3) \\ B->(-y,-x)->B^{\prime}=(1,-1) \\ C->(-y,-x)->C^{\prime}=(2,2) \\ D->(-y,-x)->D^{\prime}=(1,4) \end{gathered}[/tex]What are all the factors of 54?
To find the factors of a number, we can look for factors to divide it by subsequently.
It is easier to start with lower factors.
Let's start by "2".
Since "54" is even, it is divisable by "2":
[tex]\frac{54}{2}=27[/tex]So "2" is one of the factors.
Now, we have got 27. It is not even anymore, but it is divisable by "3":
[tex]\frac{27}{3}=9[/tex]So "3" is another factor.
Now we have got "9" and it is also divisable by "3":
[tex]\frac{9}{3}=3[/tex]So there is another "3" factor.
And since we have got now another "3", we know it is divisable by "3":
[tex]\frac{3}{3}=1[/tex]Now we have got to "1", so we found all the prime factors:
[tex]54=2\cdot3\cdot3\cdot3[/tex]Now,, we need to combine them to find all possible combinations.
We will start from low to high.
"1" is always a factor.
There is "2" there, so it is also a factor.
Then we have "3" as another factor.
There is no need to combine "1" with another factor, so we will start b combining 2 and 3:
[tex]2\cdot3=6[/tex]So, "6" is another factor.
We can combine 3 with 3:
[tex]3\cdot3=9[/tex]"9" is another factor.
Now we start combining three of them:
[tex]\begin{gathered} 2\cdot3\cdot3=6\cdot3=18 \\ 3\cdot3\cdot3=9\cdot3=27 \end{gathered}[/tex]So, "18" and "27" are factors.
And now we combine 4 of them, but this is get us back to "54" which is the last factor.
So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.
Answer:
Step-by-step explanation:
1 × 54 = 54, (1, 54) is a pair factor of 54.
2 × 27 = 54, (2, 27) is a pair factor of 54
3 × 18 = 54, (3, 18) is a pair factor of 54
6 × 9 = 54, (6, 9) is a pair factor of 54
Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).
Assume the normal distribution of data has a mean of 14 and a standard Deviation of 3. use the 65-95-99.7 rule to find the percentage of values that lie below 8
By the 65-95-99.7 rule,
[tex]\begin{gathered} 65\text{ \% of the distribution lies below }\bar{x}+\sigma\text{ and above }\bar{x}-\sigma \\ 95\text{ \% of the distribution lies below }\bar{x}+2\sigma\text{ and above }\bar{x}-2\sigma \\ 99.7\text{ \% of the distribution lies below }\bar{x}+3\sigma\text{ and above }\bar{x}-3\sigma \end{gathered}[/tex]By symmetry,
[tex]\begin{gathered} 47.5\text{ \% of the distribution lies above }\bar{x}-\sigma\text{ and below }\bar{x} \\ \text{ Hence,} \\ 2.5\text{ \% of the values lies below }\bar{x}-\sigma \end{gathered}[/tex]In our case,
[tex]\bar{x}=14,\sigma=3[/tex]Therefore,
[tex]\begin{gathered} 8=14-6=14-2(3) \\ \text{Hence,'} \\ 8=\bar{x}-2\sigma \end{gathered}[/tex]Hence, 2.5 % of the values lie below 8
The cost of renting a bicycle from Dan's Bike Shop is $2 for 1 hour plus $1 for each additional hour of rental time. Which of the following graphs shows the cost, in dollars, of renting a bicycle from Dan's Bike Shop for 1, 2, 3, and 4 hours? Bicycle Rental Cost Bicycle Rental Cost 7 6 Rental Cost (dollars) Rental Cout (dollars) 2. 1 Hetalia A B. Rental Time Chours) Bicycle Rental Cosi Bicycle Rental 7 7 Rental Cost dollars) 1 Rental Time (hours) Rental Tiene Chours) D.
option B
Explanation:The cost of renting per hour = $2
For 1 hour = $2
For each additional hour, it is $1
For 2 hours = First hour + 1(additional hour)
For 2 hours = $2 + $1(1) = 2+1 = $3
For 3 hours = $2 + $1 (2) = 2+2 = $4
For 4 hours = $2 + $1(3) = 2+3 = $5
The graph which shows this rental cost as 2, 3, 4, 5 is option B
Find the value of x that makes ADEF ~AXYZ..yE1052x – 114D11FX5x + 2Zх=
Given that the triangles are similar, we can express a proportion between their sides. DE and XY are corresponding sides. EF and YZ are corresponding sides. Let's define the following proportion.
[tex]\begin{gathered} \frac{XY}{DE}=\frac{YZ}{EF} \\ \frac{10}{5}=\frac{14}{2x-1} \end{gathered}[/tex]Now, we solve for x
[tex]\begin{gathered} 2=\frac{14}{2x-1} \\ 2x-1=\frac{14}{2} \\ 2x=7+1 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]Hence, the answer is x = 4.Solve the triangle: a = 25, C = 25, B = 25°. If it is not possible, say so.A=25*,b= 25, C = 250A=77.5*,b=10.8, C = 77.5eA=77.5', b = 24.1, C = 77.5This triangle is not solvable.
We will have the following:
First:
Since we have that sides a & c have the same length by theorem angles A & C are equal, so the following is true:
[tex]A+B+C=180\Rightarrow2A+B=180[/tex][tex]\Rightarrow2A=180-25\Rightarrow A=77.5[/tex]so, angles A & C have a measure of 77.5°.
*Second: We determine the measurement f the segment b, that is:
[tex]\frac{b}{\sin(25)}=\frac{25}{\sin(77.5)}\Rightarrow b=\frac{25\sin (25)}{\sin (77.5)}[/tex][tex]\Rightarrow b=10.8219807\Rightarrow b\approx10.8[/tex]So we will have that the measurements are:
A = 77.5°
b = 10.8
C = 77.5°
[Option B]
A granite pyramid is 50 feet high and has a square base 30 feet on a side. If granite weighs 180 pounds per cubic foot, what is the weigh in tons of the pyramid?
The weight of the granite pyramid in tons is 1350 tons.
How to find the weight of the pyramid granite in tons?A pyramid is a three-dimensional shape.
The granite pyramid is 50 feet high and has a square base of 30 feet on a side.
Granit weighs 180 pounds per cubic foot.
Therefore, the weight in tons of the pyramid can be calculated as follows;
Hence,
volume of the granite pyramid = 1 / 3 b² h
Therefore,
volume of the granite pyramid = 1 / 3 × 30² × 50
volume of the granite pyramid = 45000 / 3
volume of the granite pyramid = 15000 ft³
Hence,
1 ft³ = 180 pounds
15000 ft³ = ?
weight = 2700000 pounds
1 pounds = 0.0005 tons
2700000 pounds = ?
Therefore,
weight of the pyramid granite in tons = 1350 tons
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Find the slope using the points (2,1) and (7,5). Justify your answer
use 3.14for πThe area of the circle is
The general expression for the area of circle with radius r is express as :
[tex]\text{ Area of circle = }\Pi(radius)^2,\text{ where }\Pi=3.14[/tex]In the given circle : radius is 5ft
Substitute radius = 5 ft in the expression for the area of circle :
[tex]\begin{gathered} \text{ Area of circle = }\Pi(radius)^2 \\ Area\text{ of circle=3.14}\times5\times5 \\ \text{ Area of Circle = 78.5 ft}^2 \end{gathered}[/tex]Answer : Area of circle is 78.5 square feet
h(x)= -1/2 (x+4)^2 +10Writing quadratics in standard form
`Answer:
h(x) = -x^2/2 - 4x + 32
Explanation:
The standard form of a quadratic equation is expresssed as
ax^2 + bx+c
Writing the given equation h(x)= -1/2 (x+4)^2 +10 in stabdard form will give;
h(x)= -1/2 (x+4)^2 +10
h(x)= -1/2 (x^2+8x+16)+40
h(x)= -x^2/2 - 4x - 8 + 40
h(x) = -x^2/2 - 4x + 32
Hence the equation in standard form is expressed as h(x) = -x^2/2 - 4x + 32
What is the value of the expression 4x−y2y+x when x = 3 and y = 3? −31918
7 ( 1 + 3 )
Solve the sum inside the parentheses ( 1 + 3 = 4 )
7 ( 4 )
multiply
7*4 = 28
Since the sum must equal 28
7 + 21 = 28
Correct option = 7+21
Write the equation of a line that passes through the point (-2,-12) is parallel to the equation y= 2x +3
The most appropriate choice for equation of line in slope intercept form will be given by-
y = 2x - 8 is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line
Here,
The given equation of line is y= 2x +3
Slope of this line = 2
Slope of the line parallel to this line = 2
The line passes through (-2, -12)
Equation of the required line = y - (-12) = 2(x - (-2))
= y + 12 = 2x + 4
= y = 2x + 4 - 12
= y = 2x - 8
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Cecilia is making a punch that uses 3 quarts of fruit juice for every quart of citrus soda. How many quarts of each does she need to make 16 quarts of punch?
The number of quarts of each constituent she needs to produce 16 quarts of punch is; 12 quarts of fruit juice and 4 quarts of citrus soda.
What quantity of each constituent is needed to produce 16 quarts of punch?It follows from the task content that the quantity of each constituent that is required to make 16 quarts of punch are to be determined.
Since it follows that 3 quarts of fruit juice are required to mix with every quart of citrus soda, it follows that the amount of punch made in this scenario is; 4 quarts of punch.
Hence, since there are 4 partitions of 4 quarts punch is 16 quarts punch, the amount of.each constituent needed by proportion are as follows;
3 quarts of fruit juice × 4 = 12 quarts of fruit juice.1 quarts of fruit juice × 4 = 4 quarts of citrus soda.Read more on proportion;
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I only need help for letter b, the question is on the picture
Part B
Remember that
z =(x - μ)/(σ/√n)
where
n=21
we have
μ=1,700
σ=200
For X=1,500
Find out the value of Z1
Z1=(1,500-1,700)/(200/√21)
Z1=-4.5826
For X=1,900
Z2=(1,900-1,700)//(200/√21)
Z2=4.5826
Using a z-score table value
P(1,500therefore
The answer is 21 out of 21
Rolls are being prepared to go to grocery stores. Divide 72 rolls into 2 groups so the ratio is 3 to 5
The number of rolls divided in the two groups so that the ratio is 3 to 5 is 27 and 45 respectively.
According to the question,
We have the following information:
Rolls are being prepared to go to grocery stores.
Now, we have to divide 72 rolls into 2 groups so the ratio is 3 to 5.
Now, let's take the number of rolls given to the first group to be 3x and the number of rolls given to the second group to be 5x.
So, we have the following expression:
3x+5x = 72
8x = 72
x = 72/8
x = 9
So, the number of rolls for the first group:
3x
3*9
27
Now, the number of rolls for the second group:
5x
5*9
45
Hence, the number of rolls divided in the given two group is 27 and 45.
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Write 3.25% as a fraction in simplest form. Can you explain step by step please?
From the problem, we have 3.25% to convert into fraction.
Note that percentage a% can be written as a/100
So 3.25% will be :
[tex]3.25\%=\frac{3.25}{100}[/tex]From here, we can multiply the numerator and the denominator by 100 to make 3.25 a whole number.
[tex]\frac{3.25\times100}{100\times100}=\frac{325}{10000}[/tex]Next step is to simplify the fraction by getting the factors of the numerator and the denominator.
325 = 25 x 13
10000 = 25 x 400
Rewriting it again :
[tex]\frac{325}{10000}=\frac{25\times13}{25\times400}[/tex]Cancel the common factor (25)
[tex]\frac{\cancel{25}\times13}{\cancel{25}\times400}=\frac{13}{400}[/tex]The answer is 13/400
There are 3 consecutive even integers that sum to 186. What is the value of the greatest integer?
Answer:
The 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.
Explanation:
If the numbers are consecutive even numbers, it means that the next number will be 2 more than the previous one.
Let the 1st number be x, then other 2 consective numbers will be x + 2 and x + 4.
We're told that the sum of the 3 consecutive even numbers is equal to 186, our equation can then be written as shown below;
[tex]x+(x+2)+(x+4)=186[/tex]Let's go ahead and collect like terms and solve for x;
[tex]\begin{gathered} 3x+6=186 \\ 3x=186-6 \\ 3x=180 \\ x=\frac{180}{3} \\ \therefore x=60 \end{gathered}[/tex]So our 1st number is 60.
Let's go ahead and find the other 2 numbers;
1st number: x + 2 = 60 + 2 = 62
2nd number: x + 4 = 60 + 4 = 64
So the 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.
Boy earns 20.56 on Monday 32.90 on Tuesday and 20.78 on Wednesday he spends half what he earned during three days how much he have left
First, we need to calculate the total earned during the three days, so we need to sum 20.56, 32.90, and 20.78 as:
So, the total earned is 74.24, then half of 74.24 is calculated as:
[tex]\frac{74.24}{2}=37.12[/tex]If he spends the half, he has left the half. Therefore, he has left 37.12
Answer: 37.12
Mai must choose a number between 49 and 95 that is a multiple of 3, 8, and 12. Write all the numbers that she could choose. If there is more than one number, seperate them with commas.
Answer:
72
Explanation:
To choose a number between 49 and 95 that is a multiple of 3, 8, and 12, the first step is to find the lowest common multiple of the three numbers.
Begin by expressing them as a product of their prime factors:
[tex]\begin{gathered} 3=3 \\ 8=2^3 \\ 12=2^2\times3 \\ \text{LCM}=2^3\times3=24 \end{gathered}[/tex]Next, we find multiples of the L.C.M in between 49 and 95.
[tex]\begin{gathered} 24\times2=48 \\ 24\times3=72 \\ 24\times4=96 \end{gathered}[/tex]The only number that she could choose is 72.
Cilantro earns $17.43 per hour. If Cilantro works 27 hours in a week, what will Cilantro's earnings be for the week?
Let be "x" Cilantro's earnings (in dollars) for the week.
According to the explained in the exercise, Cilantro makes $17.43 per hour and works a total of 27 hours per week.
With that information, you can set up the following proportion:
[tex]\frac{$17.43\text{dollars}$}{1\text{hour}}=\frac{x}{27\text{hours}}[/tex]In order to find the value of "x", you need to solve for it. You can apply the Multiplication property of equality and multiply both sides of the equation by 27 hours.
Therefore, you get this result:
[tex]\begin{gathered} (27\text{hours)(}\frac{$17.43\text{dollars}$}{1\text{hour}})=(\frac{x}{27\text{hours}})(27\text{hours)} \\ x=470.61\text{dollars} \end{gathered}[/tex]Then, Cilantro's earnings for the week will be $470.61
solving right triangle find the missing side. round to the nearest tenth
Apply trigonometric functions:
Cos a = adjacent side / hypotenuse
Where:
a = angle = 59°
adjacent side = 34
Hypotenuse = x
Replacing:
Cos 59 = 34 / x
Solve for x:
x = 34 / cos 59
x = 66
Introduction to Probability
The probability of birthday being in July is 1/12.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a numeric value and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is flipping a fair (impartial) coin. The chance of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Probability of birthday being in July = 1/12 (12 months in a year)
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Solve the following logarithmic equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.)
Hello
We are given a log funtion to solve and see if it have a solution.
[tex]\log _2(x+2)=\log _2(15)[/tex]Step 1
we apply log rules
[tex]\begin{gathered} \log _2(x+2)=\log _215 \\ x+2=15 \end{gathered}[/tex]Step 2
Solve for x
[tex]\begin{gathered} x+2=15 \\ x=15-2 \\ x=13 \end{gathered}[/tex]From the calculation above, the solution of the set is 13; i.e x = 13
12/13+-1/13 equals what ?
Given:
[tex]\frac{12}{13}+(-\frac{1}{13})[/tex]Adding a negativen number is the same as subtracting that number, so:
[tex]\frac{12}{13}-\frac{1}{13}[/tex]Since both denominators (bottom number ) are equal we can subtract the numerators ( top numbers)
[tex]\frac{(12-1)}{13}=\frac{11}{13}[/tex]Answer:
[tex]\frac{11}{13}[/tex]keisha is an avid reader. One day she read for 8 hours. She read a total of 600 pages during that time. How many pages did keisha read per minute?
To find the number of page she read per minute
First let's chenge the 8 hours to minute
8 hours = 8 x 60 = 480 min
Since she read 600 pages
Number of pages read per min = 600/ 480
=1.25 pages
Tony is a hiring director at a large tech company in Chicago, and he gets hundreds of resumes each week. How long does Tony MOST likely spend looking over each resume?30 seconds50 seconds3 minutes30 minutes
The time needed to look over the resumes depends on how many papers is the resume
But it is convenient to have a speed looking on each one
so, the answe will be 50 seconds
