The Equation is 10 + x= 30 and 20 actors are from third grade.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
There are 30 actors in a school play.
There are 10 actors from second grade.
The rest are from third grade.
let the actors in third grade is x.
Equation is:
Actors from second grade + Actors from third grade = Total actors
10 + x= 30
Now, solving
Subtract 10 from both side
10 +x - 10 = 30 - 10
x = 20
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in a game a player starts with 100 points each question has two parts and a incorrect answer for both parts result in a loss of one point the student loses one half of a point for getting only one part of the question correct at the end of 25 question round the player has 82.5 points what to equations and solutions represent X Missed points
Answer:
10 questions with an incorrect answer for both parts
15 questions with a correct answer in only one part
Explanation:
Let's call x the number of questions with an incorrect answer for both parts and y the number of questions with only one part of the question correct.
So, the equation that gives us the number of points after 25 rounds is:
100 - x - 0.5y = 82.5
Where: x + y = 25
So, solving for y, we get:
y = 25 - x
Replacing this on the initial equation and solving for x, we get:
[tex]\begin{gathered} 100-x-0.5y=82.5 \\ 100-x-0.5(25-x)=82.5 \\ 100-x-12.5+0.5x=82.5 \\ 87.5-0.5x=82.5 \\ 87.5-82.5=0.5x \\ 5=0.5x \\ \frac{5}{0.5}=x \\ 10=x \end{gathered}[/tex]Then, the value of y is:
[tex]\begin{gathered} y=25-x \\ y=25-10 \\ y=15 \end{gathered}[/tex]Therefore, the player gets 10 questions with an incorrect answer for both parts and 15 questions with a correct answer in only one part.
You want to hang a picture on your wall the wall is 20 feet long you want to have at least 3 feet on both sides of the painting for plans to be placed right a quality showing the possible lanes of you being mean
We can consider
x = length of the painting
20 ft wall long
we want at least 3 ft per side so the total available length is 20-6= 14
x must be shorter than 14
inequality
x< 20-2(3)
x<14
Which inequality is equivalent to this one?y-83-2O y-8+82-2-8O y 8+82-248o y 8+22-248o Y8+ 25-242
Given the inequality:
[tex]y-8\le-2[/tex]If we add 2 on both sides, the inequality remains the same and we get:
[tex]y-8+2\le-2+2[/tex]Please help!
How many solutions does the following equation have?
6 (c+4) = 6c + 30
zero solutions
one solution
infinitely many
solutions
The number of solutions that this equation have is: A. zero solutions.
What are zero solution?Generally speaking, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal. This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out.
How to determine the number of solutions?In order to determine the number of solutions that this equation have, we would simplify the equation by opening the bracket and then compare both sides of the equation as follows:
6(c+4) = 6c + 30
6c + 24 = 6c + 30
6c - 6c = 30 - 24
0 = 6 (no solution).
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2. a) How many sets of opposite faces does this rectangular prism have? ____b) Why is the figure called a rectangular prism?
Answer:
a) 3 sets of opposite faces
b) The given figure is called a rectangular prism because its bases( the bottom face and the top face) are both rectangles.
Explanation:
a) Looking at the given rectangular prism and counting the faces, we can see that there are 6 faces in all. Out of the 6 faces of the rectangular prism, we can see that there are 3 pairs of opposite faces.
b) A prism is any 3-dimensional shape that has two identical shapes called bases facing each other.
If the two identical shapes facing each other are rectangles, then the prism is termed a rectangular prism.
Therefore, we can say that the given figure is called a rectangular prism because its bases ( the bottom face and the top face) are both rectangles.
Draw a graph, and label and scale both axes. Plot the points (-2, 3) and (1, -5), clearly labeling them.
Answer:
Explanation:
First, we draw the graph, label the x and y-axis. Then we plot the points given.
To plot the point (-2, 3), we first move to units to the left from the origin and the 3 units up as sketched below
Similarly for (1, -5), we have
We moved one unit to the right and 5 units down.
To find the slope, we take the vertical distance and the horizontal distance and then the slope will be
slope vertical distance / horizontal distance
Therefore the slope is
[tex]Slope=-\frac{8}{3}[/tex]
-ractions:
On a website, there is an ad for jeans every 5 minutes, an ad for sneakers
every 10 minutes, and an ad for scarves every 45 minutes.
If they all appeared together at 9:00 P.M., when is
the next time they will all appear together?
ICM to solve the problem
Answer:
Step-by-step explanation:
a line passes through the points (2,5) and (-6,4). What is it's equation in point-slope form?
Answer:
y-5=⅛(x-2)
Explanation:
Given the points (2,5) and (-6,4).
To find the equation of the line joining these points in point-slope form, we begin by finding its slope.
[tex]\begin{gathered} \text{Slope,m}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{5-4}{2-(-6)} \\ =\frac{1}{2+6} \\ m=\frac{1}{8} \end{gathered}[/tex]Next, we substitute the slope and any of the given points into the point-slope form below:
[tex]y-y_1=m(x-x_1)[/tex]We use the point (2,5).
• x1=2, y1=5
[tex]y-5=\frac{1}{8}(x-2)[/tex]The equation in point-slope form is y-5=⅛(x-2).
a normal distribution has mean 62 and a standard deviation 20. find and interpret the z-score for x=46
The z - score of the normal deviation will be 0.8.
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
A normal distribution has the mean = 62
Standard deviation = 20
Since, The formula for the z - score will be;
z = (x - μ) / σ
Where, σ is the standard deviation and μ is the mean of normal distribution.
Substitute all the values in above equation, we get;
z = (x - μ) / σ
z = (46 - 62) / 20
z = - 16 / 20
z = - 0.8
Therefore,
The z - score of the normal deviation will be 0.8.
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Fastex Shoes claims that it has designed a new range of lightweight shoes that allow athletes to run faster than they can using any other shoes.SportsPlus, a rival shoe manufacturer, then came up with a design that it claims performs even better than Fastex's design. A sports magazinedecided to test the claims. It created two groups of 15 randomly selected athletes each. Members of both groups were pretested anddetermined to have equal athletic ability. Additionally, they followed the same nutrition plan and training program during the study.The athletes did a 1-mile run to test the shoes. The magazine found that the athletes who used Fastex shoes had reduced their 1-mile run timeby an average of 396, and athletes who used Sports Plus shoes had reduced their 1-mile run time by an average of 2%.Given the magazine's data collection method and findings, what conclusion can be made?OA. The data collection method used was fair since both shoe designs were tested on identical parameters.OB. The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.OC. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than theathletes given SportsPlus shoes.OD. The data collection method used was random since the athletes in the two groups used two different shoe designs.
B: The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.
This is false because they followed the same nutrition plan and training program during the study.
C. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than the athletes given SportsPlus shoes.
This is also false because members of both groups were pretested and determined to have equal athletic ability
D. Each group used one shoe design.
So, the correct option is A
A periodic deposit is made into an annuity with the given terms. Find how much the annuity will hold at the end of the specified amount of time. Round your answer to the nearest dollar.Regular deposit:$1300Interest rate:4.2%FrequencyannuallyTime:17 yearsFuture value: $
SOLUTION
We will use the formula
[tex]FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack[/tex]Where FV represents the future value annuity
P = Periodic payment = 1300
r = interest rate = 4.2% = 0.042
n = number of periods = 17 years.
So we have
[tex]\begin{gathered} FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack \\ FV=1300\lbrack\frac{(1+0.042)^{17}-1}{0.042}\rbrack \\ FV=1300\lbrack\frac{(1.042)^{17}-1}{0.042}\rbrack \\ FV=31,341.485 \end{gathered}[/tex]Hence, the answer becomes $31,341 to the nearest dollar
In the triangle below, suppose that mZH= (6x-4)°, mZ1 = (2x-5)°, and m
Find the degree measure of each angle in the triangle.
(2x - 5) ⁰
H (6x-4)
x
mZH =
m 41 =
mZJ =
1
X
Answer: H = 122, I = 37, J = 21
Step-by-step explanation:
All the angles of a triangle add up to 180 degrees.
(6x - 4) + (2x - 5) + x = 180
Combine like terms
9x - 9 = 180
Solve for x
9x = 189
x = 21
m<H = (6*21 - 4) = 122
m<I = (2*21-5) = 37
m<J = 21
Hi, the area of a circle is 100 sq. mm. The radius is 5.64 mm. What is the circumference?
11.28π mm
1) Since the area is 100 mm² we can plug into the Circumference formula to find out the perimeter of that circle
2)
[tex]\begin{gathered} C=2\pi\cdot r \\ C=2\cdot\pi\cdot(5.64)^{} \\ C=11.28\pi \end{gathered}[/tex]3) Hence, the circumference of that circle is 11.28π mm
Find the lateral area of the cylinder .The lateral area of the given cylinder is _ M2(Round to the nearest whole number as needed .)
The lateral area of a cylinder is:
[tex]LA=2\pi rh[/tex]r is the radius
h is the height
For the given cylinder:
As the diameter is 4m, the radius is half of the diameter:
[tex]r=\frac{4m}{2}=2m[/tex]h=12m
[tex]\begin{gathered} SA=2\pi(2m)(12m) \\ SA=48\pi m^2 \\ SA\approx151m^2 \end{gathered}[/tex]Then, the lateral area of the given cylinder is 151 square metersForm a polynomial whose zeros and degree are given.Zeros: -4, multiplicity 2; -3, multiplicity 1; degree 3O x3 + 8x2 + 40x + 48O x3 - 11x2 + 24x - 48O x3 + 11x2 + 40x + 48O x3 - 11x2 + 40% - 48
.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
Determine whether the graph shown is the graph of a polynomial function
the given graph is smooth and its domain is containing all real numbers
so it is a polynomial function.
Choose the correctdomain for thequadratic function.А-00 > X < 0B-00 < x < 0
The function given in the graph stretches from negative to positive infinity.
Hence the domain of the function is given by:
[tex]-\inftyOption B is correct.which of the following circles have their centers in the second quadrant
The circles in option B and D has their centers in the second quadrant
Here, we want to know which of the circles have their centers in the second quadrant
Generally, the equation of a circle can be represented as;
[tex](x-h)^2\text{ + (y-}k)^2=r^2[/tex]where (h,k) represents the center of the circle
Now, let us get the center of each of the circles;
A. (4,-3)
b. (-1,7)
C.(5,6)
D. (-2,5)
The second quadrant has its coordinates in the form (-x,y)
Out of all the options, the option that fits these quadrant is the second and fourth
So the circles in option B and D has its center in the second
Help please I’ll give 10 points
Choose the right symbol for the following
What are Symbols?
Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.
1) 0.02 > 0.002
2) 0.05 < 0.5
3) 0.74 < 0.84
4) 0.74 > 0.084
5) 1.2 < 1.25
6) 5.130 = 5.13
7) 3.201 > 3.099
8) 0.159 < 1.590
9) 8.269 > 8.268
10) 4.60 > 4.060
11) 302.026 > 300.226
12) 0.237 > 0.223
13) 3.033 < 3.303
14) 9.074 < 9.47
15) 6.129 < 6.19
16) 567.45 > 564.75
17) 78.967 > 78.957
18) 5.346 < 5.4
19) 12.112 < 12.121
20) 26.2 = 26.200
21) 100.32 > 100.232
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Which interval notation represents a function with a domain of all real numbers greater than or equal to 4?A.) -35 D.) y>0 E.) Y<4
If the domain is all real numbers greater than or equal to 4, the interval will be
[tex]x\ge4[/tex]what kind of triangle congruence would i put for the last reason?
Looking at the diagram, The last statement means that trangle PQS is congruent to triangle RSQ. This means that
line PQ is equal to line RS
line QS is equal to line SQ
angle Q is equal to angle S
Thus, the reason would be
Side Angle Side(SAS)
Two sides and one angle are equal or congruent
Find percent change of 50 to 43
Answer:
-14.00%
Step-by-step explanation:
((43-50)/50)*100 = -14.00%
←
In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
The probability of being a girl child to a couple is 0.9498
Yes, this technique appear effective in improving the likelihood of having a female baby
Given,
In a sex selection technique,
The number of female babies in the result = 284
The number of male babies in the result = 15
Total children = 284 + 15 = 299
We have to find the probability of being a girl child;
Probability;
Probability refers to potential. Probability values are limited to the range of 0 to 1. Its fundamental notion is that something is probable to occur. It is the proportion of favorable events to all other events.
Here,
The probability of being a girl child, P = 284/299 = 0.9498
That is,
The probability of being a girl child to a couple is 0.9498
Yes, this technique appear effective in improving the likelihood of having a female baby
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You want to build a sandbox that can hold50,445 cubic inches of sand. If the sandbox is to be59 in. long and57 in. wide, how tall will it need to be?
Volume of sandbox (to be built) = 50,445 cubic inches
A sandbox is the shape of a cuboid and is calculated by the formula
[tex]\text{volume = length }\cdot\text{ wi}\differentialD tth\text{ }\cdot\text{ height }\Rightarrow\text{ v = l }\cdot\text{ w }\cdot\text{ h}[/tex]Volume = Length * Width * Height
Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?
50,445 = 59 * 57 * h
Make h the subject of the formula, we have:
h = 50445 / (59 * 57) = 15 in
PLEASE help I'll send a picture in later.
Given
Table of names
Procedure
Names end with an E
Gabe
Steve
The probability would be independent and equal to:
[tex]\begin{gathered} \frac{2}{6}\cdot\frac{2}{6} \\ \frac{4}{36} \\ \\ \frac{1}{9} \end{gathered}[/tex]The probability would be 1/9
A box is filled with shoe boxes. Each shoe box has a volume of 1 cubic foot. Six shoe boxes can fit in each layer and the height of the box is 4 feet. What is the volume of the box?
shoe box = 1 cubic foot = 1 * 1 * 1
1 Layer: 6 shoe boxes -> Layer lenght = 6 feet, layer depht = 1 foot
Box height = 4 feet
Box volume = 6*4*1 = 24 feet
Which of the following is the number of sides a polygon can have to form aregular tessellation?O A. 9B. 3C. 5D.7
From the image, we are asked the number of sides a polygon can have to form a regular tesselation.
The first step is to understand what a regular tessellation is;
A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape. There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons.
This implies that it could either have 3 sides(triangle), four sides(square), six sides(hexagon).
From the given options we can clearly see that 3 sides is the only available option.
ANSWER: Option B
Lloyd is standing near a telephone pole. When his head touches the support wire, he is 25 feet from where the wire meets the ground. Lloydis 5 ft tall. Hon tallis the pole?1-8f feetO A 20 ft.B. 15 ftC. 80 ft.D. 17 ft
We will use the pythagorean theorem to figure the answer out.
Applying the Pythagorean Theorem, we have (let unknown side be x):
[tex]\begin{gathered} 6^2+x^2=10^2 \\ 36+x^2=100 \\ x^2=100-36 \\ x^2=64 \\ x=\sqrt[]{64} \\ x=8 \end{gathered}[/tex]Answer 8 feet (B)14|x + 14| + 13 =-69
Solve for x
Answer: No real solutions
Step-by-step explanation:
[tex]14|x+14|+13=-69\\\\14|x+14|=-82\\\\|x+14|=-82/14[/tex]
Since absolute value is always non-negative, there are no real solutions.
