1st = 12 stickers
2nd = 18 stickers
3rd = 30 stickers
Explanation:Total stickers = 60
Ratio of the three students = 2:3:5
Let the ratio of the 1st student = 2
The ratio of the 2nd student = 3
The ratio of the 3rd student = 5
Total ratio = 2 + 3 + 5 = 10
[tex]\begin{gathered} \text{The amount each student gets = }\frac{ratio}{\text{total ratio}}\times\text{ total stickers} \\ \end{gathered}[/tex][tex]\begin{gathered} 1st\text{ student = }\frac{2}{10}\times60 \\ 1st\text{ student = 12 stickers} \end{gathered}[/tex][tex]\begin{gathered} 2nd\text{ student = }\frac{3}{10}\times60 \\ 2nd\text{ student = 18} \end{gathered}[/tex][tex]\begin{gathered} 3rd\text{ student = }\frac{5}{10}\times60 \\ 3rd\text{ student = }30\text{ stickers} \end{gathered}[/tex]if the legs of a right triangle are 10 and 24 then the hypotenuse is
Since we have that the legs of the right triangle are 10 and 24, then we can use the Pythagorean Theorem to find the hypotenuse as follows:
[tex]h^2=10^2+24^2=100+576\Rightarrow h^2=676\Rightarrow h=\sqrt[]{676}\Rightarrow h=26[/tex]Therefore, the hypotenuse has a value, in this case, of h = 26 units.
Solve 9x – 5 = (16x + 60)Select one of the equations above and explain two different ways that you could go about solvingit.
To solve the equation you should separate x on one side and the number on the other side, then make the coefficient of x = 1
Let us do that
Multiply the bracket by 1/4 first
[tex]\frac{1}{4}(16x+60)=\frac{1}{4}(16x)+\frac{1}{4}(60)=4x+15[/tex]So the equation will be
9x - 5 = 4x + 15
Add 5 to both sides to move 5 from the left hand to the right hand
9x - 5 + 5 = 4x + 15 + 5
9x = 4x + 20
Now subtract 4x from both sides to move x
Find angle X. Round to 2 decimal places. cos X=0.4477
Answer:
X=63.4°
Explanation:
Given:
[tex]\cos X=0.4477[/tex]Find the arccosine of both sides:
[tex]\begin{gathered} \arccos(\cos X)=\arccos(0.4477) \\ X=63.4038\degree \\ X\approx63.40\degree \end{gathered}[/tex]The value of angle X is 63.4° (rounded to 2 decimal places).
A number (z) is equal to 192 decreased by 15 times the number. What is the value of z?
The value of z is 12
Explanation:The given statement is interpreted as follows:
z = 192 - 15z
Add 15z to both sides
z + 15z = 192
16z = 192
Divide both sides by 16
z = 192/16
= 12
1.Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2.
The equation is:
[tex]y+3=\frac{1}{2}(x-6)[/tex]Explanation:Given that the line has slope of 1/2, and passes through th e point (6, -3), the equation in point-slope form is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \\ \text{where} \\ x_1=6 \\ y_1=-3 \\ m=\frac{1}{2} \end{gathered}[/tex]This becomes:
[tex]\begin{gathered} y-(-3)=\frac{1}{2}(x-6) \\ \\ y+3=\frac{1}{2}(x-6) \end{gathered}[/tex]Select the correct answer from each drop-down menu.A high school choir is holding a fundraiser for its spring contest trip. The amount each student needs to raise varies as the number of studentswho participate in the fundraiser. If 50 students participate in the fundraiser, each student needs to raise $275.Use this information to complete the statements.
Given:
A high school choir is holding a fundraiser for its spring contest trip. The amount each student needs to raise varies as the number of students
who participate in the fundraiser. If 50 students participate in the fundraiser, each student needs to raise $275.
Required:
Complete the statements.
Explanation:
Part 1:
1. The proportional situation represents inverse variation
This is because, the total amount that they hope to raise is the same regardless of the number of students
Part 2:
[tex]\begin{gathered} K=SA \\ K=50\times275 \\ K=13.750 \end{gathered}[/tex]The constant of variation, k, is equal to $13,750.
Part 3:
[tex]\begin{gathered} K=SA \\ A=\frac{K}{S} \\ A=\frac{13750}{100} \\ A=137.5 \end{gathered}[/tex]If all 100 students in choir participate in the fundraiser, each will need to raise $137.5.
Answer:
answered the statements.
Give a standard deck of 52 cards, what is the probability of randomly drawing a card and the card is red? Round your answer two decimals
Given a standard deck of 52 cards, we must find the probability of randomly drawing a red card. We know that:
• # of red cards = 26,
,• # of cards in the deck = 52.
The probability of drawing a red card is given by:
[tex]P(\text{red card)}=\frac{\#\text{of red cards}}{\#\text{of cards in the deck}}=\frac{26}{52}=0.5.[/tex]Answer
The probability of randomly drawing a red card is 0.5 or 50%.
5. AFGH with F(-6,8), G(-3,-1), and HCO, 4); reflect across the x-axis, then reflect across the line y = -x 12 a. What are the two arrow rules to show this composition? 76 b. What are the vertices of the image after the composition?
We are asked to reflect the vertices of a triangle first across the x-axis and then across the line y = -x. The rule for a reflection across the x-axis is the following:
[tex](x,y)\rightarrow(x,-y)[/tex]Or
[tex]R_x(x,y)=(x,-y)[/tex]The rule for the reflection across the line y = -x:
[tex](x,y)\rightarrow(-y,-x)[/tex]Therefore, applying both transformations we get:
[tex](x,y)\rightarrow(x,-y)\rightarrow(y,-x)[/tex]Applying the rule to each point.
For point F(-6,8) we get:
[tex](-6,8)\rightarrow(-6,-8)\rightarrow(8,6)[/tex]For point G(-3,-1):
[tex](-3,-1)\rightarrow(-3,1)\rightarrow(-1,3)[/tex]For point H(0,4) we get:
[tex](0,4)\rightarrow(0,-4)\rightarrow(4,0)[/tex]
The value of y is inversely proportional to the value of x. When y = 42, x = 6. What is the value of y when x = 9? 45, 28, 63, 252
1) We know that an inversely proportional variation can be written as:
[tex]y=k(\frac{1}{x})[/tex]2) Note that we were also told that when y= 42, x=6 so let's find the quantity of k:
[tex]\begin{gathered} y=k(\frac{1}{x}) \\ 42=k(\frac{1}{6}) \\ 42=\frac{k}{6} \\ k=252 \end{gathered}[/tex]2.2) Now, let's find the quantity of y when x=9:
[tex]\begin{gathered} y=k(\frac{1}{x}) \\ y=252\cdot(\frac{1}{9}) \\ y=28 \end{gathered}[/tex]Thus, the answer is y=28
In a circle, an angle measuring 3 radians intercepts an arc of length 13. Find theradius of the circle to the nearest 10th.
Normally, when we want to find the arc of length given a radius and an angle we use the next equation:
[tex]S=rθ[/tex]where:
s represents the arc of length
r represents the radius
θ represents the angle
We need to find the radius, so we need to solve for r:
[tex]r=\frac{s}{θ}[/tex]Replace using θ=13 rad and s=13
Then:
[tex]undefined[/tex]f(x) = (3x ^ 2 + 6x + 3)/(sqrt(x)) then :
Given: A function's derivative is given:
[tex]f^{\prime}(x)=\frac{3(3x-1)(x+1)}{2x^{\frac{3}{2}}}[/tex]Required: To determine the value of f'(3).
Explanation: The value of f'(3) can be determined by substituting x=3 in f'(x) as follows-
[tex]f^{\prime}(3)=\frac{3[(3\times3)-1](3+1)}{2\times3^{\frac{3}{2}}}[/tex]Further solving,
[tex]\begin{gathered} f^{\prime}(3)=\frac{3\times8\times4}{2\times3^{\frac{3}{2}}} \\ =\frac{16}{3^{\frac{1}{2}}} \end{gathered}[/tex]On further solving the equation, we get
[tex]\begin{gathered} f^{\prime}(3)=\frac{16}{1.7321} \\ =9.2376 \end{gathered}[/tex]Final Answer:
[tex]f^{\prime}(3)=9.2376[/tex]solve each system of equations below by graphing, please use my graphy= -2y= 2/5x-4
Let's graph the following system of equations.
y = -2 (Equation 1)
y = 2/5x - 4 (Equation 2)
First, let's determine the coordinates of two points that pass through the graph of Equation 2. These points will serve as our guide as we make its graph.
We get,
y = 2/5x - 4
Point 1: (0, -4)
x = 0
y = 2/5(0) - 4 = -4
Point 2: (10, 0)
y = 0
0 = 2/5x - 4
4 = 2/5x
4 x 5 = 2x
20/2 = x
10 = x
Let's now plot the graph.
Plotting the graph of the two systems of equations, they will be intersecting at (5, -2).
y = 6 - x; (-3,3)
is it a solution?
Answer: No
Explanation:
The given equation is
y = 6 - x
To determine if (- 3, 3) is a solution, we would substitute x = - 3 into the equation. If we get y = 3, then it's a solution. We have
y = 6 - - 3
y = 9
Since y ≠ 3,
(- 3, 3) is not a solution
8-12x-10+7x simplified
Step 1. The expression that we have is:
[tex]8-12x-10+7x[/tex]Required: Simplify the expression.
Step 2. To simplify, we need to combine like terms.
Like terms are the ones that have the same variable, in this case -12x and 7x are like terms, and when we combine them -12x+7x the result is -5x:
[tex]8-12x-10+7x=8-10-5x[/tex]Step 3. The independent terms 8 and -10 are also like terms and we can combine them: 8-10 is equal to -2. Therefore, the final result is:
[tex]-2-5x[/tex]We can put the variable term first:
[tex]-5x-2[/tex]Answer:
[tex]\boxed{-5x-2}[/tex]what is the prime number
The prime number is the number that has 2 divisible numbers (two factors), one and itself
For example, 2 is a prime number it can be divide by 1 and 2
Examples:
3, 5, 7, 11, .......
Match the base to the corresponding height. Base (b) Height (h) b h 109%7 b b h
In the question, we have three cases. We need to know that the base must be perpendicular to the height of the triangle. In this case, we see that option 3 is the one that fulfills this requirement. Then, we have:
which of the following measurements are a little bit more thsn a yard?metercentiliter1/4 footcenitimeter
As we know that, 1 yard = 0.9144 m
1 foot = 0.305 m
1/4 foor = 0.076125 m
1cm = 0.01 m
The measurement which is a little bit more than a yard is meter.
Answer: Option (b) that is meter
Find each angle measure in the figure. Write an equation so that the sum of the angles is 180. 4y + 20 + y - 10 = 180 4y (y - 10) 20°
Interior angles of a triangle add up to 180, this imply that
[tex](y-10)+4y+20=180[/tex]Now, by combining similar terms, we have
[tex]y+4y-10+20=180[/tex]which gives
[tex]5y+10=180[/tex]If we movw +10 to the right hand side as -10, we obtain
[tex]\begin{gathered} 5y=180-10 \\ 5y=170 \end{gathered}[/tex]then, y is equal to
[tex]\begin{gathered} y=\frac{170}{5} \\ y=34 \end{gathered}[/tex]Now, we can substitute this values in order to find the measure of each angle:
[tex]\begin{gathered} (y-10)\Rightarrow34-10=24 \\ \text{and} \\ 4y\Rightarrow4(34)=136 \end{gathered}[/tex]Therefore, the angles are 24, 136 and 20 degrees.
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
xy
110
28
36
44
Initial value: 12, rate of change: −2
Initial value: 8, rate of change: 2
Initial value: 12, rate of change: 2
Initial value 8, rate of change: −2
Remember that
In a linear equation
y=mx+b
the rate of change is the same that the slope m
and the initial value is b
so
step 1
Find out the slope
we take the points (2,3) and (4,5)
m=(5-3)/(4-2)
m=2/2
m=1
step 2
Find out the equation of the line
y=mx+b
we have
m=1
point (2,3)
substitute and solve for b
3=(1)(2)+b
3=2+b
b=1
therefore
The rate of change is 2 and the initial value is 1Can you answer (b) and (d) on number 27 please?
To find:
b) measure of angle 1
d) If AC = 10, then DE = ?
Solution:
b) Given that ABCD is a square. It is known that the interior angle of a square is equal to 90 degrees and the diagonal bisects the interior angles of the square. So, angle 1 is equal to 45 degrees.
Thus,
[tex]m\angle1=45^o[/tex]d) The diagonals of a square are equal in length. If AC = BD = 10 cm.
The diagonal of a square bisect each other. So, BE = ED = 5 cm.
Thus, DE = 5 cm.
A softball player has hit a ball into the air. The height, y, of the ball x seconds after it is hit is given byy= -16.x2 + 78x +3.25.-What is the initial height of the softball? | Select ]-How long was the softball in the air? [Select]-What is the maximum height of the softball? | Select ]-How long did it take for the softball to reach its maximum height? Select]
The given function is
[tex]y=-16x^2+78x+3.25[/tex]To answer the questions, we draw the function. The image below shows the graph.
The initial height of the softball is 3.25 because that's the height when x = 0, let's prove it.
[tex]\begin{gathered} y=-16(0)^2+78(0)+3.25 \\ y=0 \end{gathered}[/tex]As you can observe in the image, the softball was 5 seconds in the air, the x-intercept shows the moment when the softball reaches the ground.
The maximum height is 98.313 because that's the point where the ball stops and goes down.
The softball took 2.5 seconds to reach the maximum height.
There are 9 athletes at a track meet. How many different ways can they finish first or second?
for the first place we have 9 options, and once you have the first one, there are 8 options left for the second place, so we have:
[tex]9\cdot8=72[/tex]72 different ways for first and second.
Frank spent a total of $65 at the grocery store. Of this amount, he spent $39 on fruit. What percentage of the total did he spend on fruit?
We know that
• Frank spent a total of $65.
,• He spent $39 on fruit.
To know the percentage of fruit, we just have to divide them, then we multiply by 100 to express it in percentage
[tex]\begin{gathered} f=\frac{39}{65}=0.6 \\ f=0.6\cdot100=60 \end{gathered}[/tex]Therefore, Frank spent 60% of his money on fruit.if you could give me the answer without explanation because im on a tight schedule i would love to leave a good reveiw thanks!
We have to prove that ABDC is a parallelogram.
3) The third step is the reflexive property, where BD = BD (equal to itself). This let us to the following step, where we state that the 2 triangles are congruent.
4) Triangle ABD is congruent to triangle CBD, by the SSS postulate.
5) <1 = <3, as they are alternate interior angles between parallels.
6) <2 = <4, as they are alternate interior angles between parallels.
7) AB || CD
8) AD || BC
9) ABCD is a parallelogram as its opposite sides are congruent.
Question 1: how do I find the coordinate of B prime after the reflection? Question 2: how do I find the coordinate of a prime after the rotation
When reflection is done across the y coordinate, the point on the y axis is left unchanged while the point on the x axis is mirrored(the sign is reversed)
For the point B on the graph, the original coordinate is (- 2, -1)
Since it is reflected across the y axis, only the sign on the x coordinate would the reversed. Therefore,
the coordinate of B prime is (2, -1)
option D is correct
D. $1,907.50 A rectangular print is 36 inches long and 24 inches wide. It will be placed inside a rectangular frame that is 2 inches wide on all sides. What is the area when the print is inside the frame?
Given A rectangular print is 36 inches long and 24 inches wide.
And a rectangular frame that is 2 inches wide on all sides.
so, the rectangular frame will be 38 inches long and 26 inches wide.
The area of the rectangular print = 36 x 24 = 864 square inches
The area of the rectangular frame = 38 x 26 = 988 square inches
The area when the print is inside the frame will be the area of the frame
So, the answer will be 988 square inches
A third of my number is 7. what is my number
A third of my number is 7, then my number must be 21.
How to solve a missing number?Identify whether the given numbers are in ascending (smaller to larger) or descending order ( larger to smaller number).Different kinds of numerical patterns exist.
Arithmetic progression.Geometric Order.Square figures.Number Cubes.Triangle-shaped numbersa Fibonacci sequence.So, now determine the variations between the objects that are next to one another.
Calculate the missing number by estimating the difference between the two numbers.
By substituting x for the unknown in the equation, the following can be done:
1/3 × x = 7Add three to both sides:
1 × x = 21\sx = 21The quantity has to be 21.Therefore, a the third of my number is 7, then my number must be 21.
To learn more about missing numbers refer to:
brainly.com/question/23171011
#SPJ1
I am having a tough time solving this step by stepI have attempted this but I’m not sure if I’m correct, and need some more clarification
Given -
ΔEFG is right angle at F
EG = 8
FG = 6
To Find -
cotG =?
SinE =?
SecG =?
Step-by-Step Explanation -
According to the question -
Now, we will find the value of EF -
(EF)² + (FG)² = (EG)²
(EF)² + (6)² = (8)²
(EF)² = 64 - 36
(EF)² = 28
EF = 2√7
Now,
CotG = 2√7/6 = √7/3
SinE = 6/8 = 3/4
SecG = 8/6 = 4/3
Final Answer -
CotG = √7/3
SinE = 3/4
SecG = 4/3
Determine if JK and LM are parallel, perpendicular, or neither. J(1, 9), K(7, 4), L(8, 13), M(-2, 1).
First of all, we need to remember two statements:
1) two lines are perpendicular when the product of its slopes is equal to -1.
2) two lines are parallel when they have the same slope.
Now, we need to find the slope for both lines, we start with the segment of line JK
[tex]\begin{gathered} m=\text{slope}=\frac{(y_2-y_1)}{(x_2-x_1)};\text{ } \\ J(1,9)=J(x_1,y_1);x_1=1;y_1=9 \\ K(7,4)=J(x_2,y_2);x_2=7;y_2=4 \\ m=\text{slope}=\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{(4-9)}{(7-1)}=\frac{-5}{6} \\ m=\frac{-5}{6} \end{gathered}[/tex]In the same way, we need to find the value of the slope to the segment LM
[tex]\begin{gathered} m=\text{slope}=\frac{(y_2-y_1)}{(x_2-x_1)}; \\ L(8,13)=L(x_1,y_1);x_1=8;y_1=13 \\ M(-2,1)=M(x_2,y_2);x_2=-2;y_2=1 \\ m=\text{slope}=\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{(1-13)}{(-2-8)}=\frac{-12}{-10}=\frac{6}{5} \\ m=\frac{6}{5} \end{gathered}[/tex]From that we can conclude that both segments are NOT parallel,
Now, we verify if they are perpendicular multiplying the slopes, like this:
[tex]\frac{-5}{6}.\frac{6}{5}=-1[/tex]Finally, we conclude that both segments are parallel because the product of its slopes are -1.
ise the data above to construct a pie chart. include the relative frequenxy, the percent , and the angels in your information
Solution
The total frequency is:
3+ 7+16+ 20+ 23 =69
The relative frequency for this case is:
zinnias= 3/69 = 0.0435 = 4.35%
gladiolas = 7/69= 0.101 = 10.1%
marigold = 16/69= 0.232 = 23.2%
hollyhocks = 20/69= 0.290 = 29.0%
lilies = 23/69= 0.333 = 33.3%