68 = Diane's score x 4
Equation
68= 4d
___________________
Can you see the updates?
_________________
Diane's score
4d= 68
d= 17
"Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?" Please help meee
Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?
Let
x ------> students enrolled last year
we have that
100%+10%=110%=110/100=1.10
so
528=1.10x
solve for x
x=528/1.10
x=480
answer is 480 studentsWhat is the value of pi
Answer:
the value of pi is 3.14159
Which postulate proves the two triangles congruent?
A. SSS
B. SAS
C. ASA
D. AAS
Answer:
A. SSS
Step-by-step explanation:
Triangle ADT and triangle TDE are congruent triangles by SSS postulate.
Sides DE and DA, sides TE and TA are congruent (DT is common side).
So the answer is A. SSS
Can someone please help answer this question on simultaneous equations?
Answer:
1 knife cost £6.6
Step-by-step explanation:
Simultaneous equation is;
4x = y ----------(equation 1)
12y + 16x = 105.64 ----------- (equation 2)
Rewrite equations:
4x=y;16x+12y=105.64
Step: Solve4x=yfor y:
4x=y
4x+−y=y+−y(Add -y to both sides)
4x−y=0
4x−y+−4x=0+−4x(Add -4x to both sides)
−y=−4x
−y/−1 = −4x/−1
(Divide both sides by -1)
y=4x
Step: Substitute 4x for y in 16x+12y=105.64:
16x+12y=105.64
16x+124x=105.64
64x=105.64(Simplify both sides of the equation)
64x/64 = 105.64/64
(Divide both sides by 64)
x=1.650625
Step: Substitute 1.650625 for x in y=4x:
y=4x
y=(4)(1.650625)
y=6.6025(Simplify both sides of the equation)
1 knife cost = 4x = 4(1.65) = 6.6
∴ 1 knife cost £6.6
Given :R is the midpoint of QSQR = 6x - 9 RS = 2x - 1 We need to find QS
Given :
R is the midpoint of QS
QR = 6x - 9
RS = 2x - 1
We need to find QS
So, as R is the midpoint
[tex]\begin{gathered} QR=RS \\ 6x-9=2x-1 \end{gathered}[/tex]Solve the equation to find x :
[tex]\begin{gathered} 6x-9=2x-1 \\ 6x-2x=-1+9 \\ 4x=8 \\ \\ x=\frac{8}{4}=2 \end{gathered}[/tex]Substitute with x to find QR and QS
[tex]\begin{gathered} QR=6\cdot2-9=12-9=3 \\ RS=2\cdot2-1=4-1=3 \\ \\ QS=QR+RS=3+3=6 \end{gathered}[/tex]Find the area of the entire region round two decimal places
SOLUTION.
The area of the entire region will be to find the area of the isosceles triangle and the semi-circle.
[tex]\begin{gathered} \text{Area of the triangle is } \\ =\frac{1}{2}\times a\times b\times\sin \theta \\ \text{Where } \\ \text{where a and b are two sides and }\theta=angle\text{ betwe}en\text{ the two sides } \end{gathered}[/tex]Then
[tex]\begin{gathered} =\frac{1}{2}\times8\times8\times\sin 72.6 \\ =32\sin 72.6 \\ =30.54\text{unit}^2 \end{gathered}[/tex]The area of the isosceles triangle is 30.354 square units
We need to obtain the diameter of the semi-circle using the cosine rule
We need to obtain the value of x,
[tex]\begin{gathered} x^2=8^2+8^2-2(8)(8)\cos 72,6 \\ x^2=128-128\cos 72.6 \\ x^2=128-38.27 \\ x^2=89.72 \end{gathered}[/tex]Take square root of both sides, we have
[tex]x=\sqrt[]{89.72}=9.74[/tex]Hence, the diameter is 9.74
Then the radius will be
[tex]r=\frac{9.74}{2}=4.87[/tex]The area of the semi-circle is
[tex]\begin{gathered} =\frac{1}{2}\pi r^2 \\ =\frac{1}{2}\times3.14\times4.87^2 \\ =37.24\text{unit}^2 \end{gathered}[/tex]The area of the semi circle is 37.42 square units
Therefore the area of the region will be
[tex]\begin{gathered} =\text{Area ot triangle + Area of semi circle } \\ =30.54+37.42 \\ =67.96uniits^2 \end{gathered}[/tex]Thus
The area of the region is 67.96 units²
A fair quarter, a fair dime, a fair nickel, and a fair penny are tossed. Find the probability of obtaining exactly one head.
We know that the probability of getting a head in a single coin is:
[tex]p=0.5[/tex]Now, we can calculate the probability of X out of N coins landing heads up with the binomal distribution:
With p = 0.5 and N = 4, we get:
Subtituting X = 1 ("getting one head"), we get that:
[tex]P=0.0625[/tex]A line contains the points (-21,-94) and
(-34,-172).
What is the slope of the line in simplified form?
v - 4 > 22 solve the inequality of v and simplify your answer as much as possible. plsssss do this!!!
Answer:
v > 26
Step-by-step explanation:
v > 22 + 4
v > 26
there is no qouificient ( I don't know how to spell that) of v so that's your answer
Jonah and Makayla are on a scuba diving tour of a reef. Jonah is at a depth of –20 feet and ascending at a rate of 0.25 foot per second. Makayla is at a depth of –12.5 feet and descending at a rate of 0.5 foot per second. Solve the equation 2(−20+0.25s)=−12.5−0.5s to find how many seconds s it will take for Makayla to be twice as deep as Jonah. Enter your answer as an integer or decimal.
It will take 28.5 seconds to Makayla to be twice as deep as Jonah.
What is an equation?
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15.
Given,
Jonah is at a depth of -20ft.
Makayla is at a depth of -12.5ft.
at the rate of descending is 0.5.
Given equation is
2(-20+0.25s) = -12.5-0.5s
-40 + 0.5 s = -12.5 -0.5s
0.5s + 0.5s = -12.5+40
1s = 28.5
Hence, the solution of the equation is 1s = 28.5.
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Determine the missing coordinate in the orderd pair (?,-3) so that it will satisfy the given equation. Answer: (______,-3). consider the following equation.4x+3y=7
if we replace y for -3 in the given equation and then we despejate x, we wiil going to have a values for the ordered pair that satisfy the equation:
[tex]4x+3(-3)=7[/tex]then
[tex]4x-9=7\Rightarrow4x=7+9\Rightarrow4x=16\Rightarrow x=\frac{16}{4}=4[/tex]the ordered pair woul be (4,-3)
3. a sociologist wishes to estimate the percentage of u.s. citizens living in poverty. what sample size should be obtained if she wishes the estimate to be within 2% points (the error) with 99% confidence if she uses the year 2000 estimate of 11.8% poverty obtained from the census?
The sample size is 1727 points for given data . Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population .
In this question we want to find the sample size and so let's, look at the formula that is given by, the value at over 2, divided by a margin of error, whole squared times p into 1 minus p.
N= ( Z ₐ / E)² p (1-p)
In this case , Z --> Z-Score
E --> error value
P --> estimated proportion or if given standard deviations
Given that, estimate error is 2% that is margin (E) = 2% = 2/100 =0.02
Now, what we have is our confidence level and our made error, so our estimate has been given us 2 percent or confidence level is 99 percent. Now, let's get our Z values, so we use alpha(a) to find out. For alpha value 1 minus 0.99 , we get 0.01. now we are going to be 0.01 divide by 2 and get 0.005 . So, the corresponding value of Z ₀.₀₀₅ is 2.576 . The only value of p is 11.8% (year 2000 estimate ) of what is required for getting an answer
= 118/1000= 0.118
Finally, we put all these values into formula of sample size , i.e.,
N= ( 2.576 / 0.02)² (0.118 )(1- 0.118) = 1726.56 1727
Our sample size is , 1727 point.
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Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for bagels, then walks the rest of the way home. What does the X axis represent. What does the y-axis represent?
Based on the information provided about Arthur, we have the following:
The x-axis of the graph would represent the amount of time that Arthur spends on his way home.The y-axis of the graph would represent the distance covered by Arthur from a reference position (home).What is a graph?In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate).
What is distance?Distance simply refers to the amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of the physical object's direction, starting point, or ending point.
In conclusion, the distance covered by a physical object (body) over a particular period of time can be plotted by using a position-time graph as shown in the image attached below.
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(2,-9) reflected over the y-axis
The new point is (-2, -9).
What happens when a point is reflected about an axis?
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given, the point to be reflected is : A : (2, -9)
Also, the axis through which the point is to be reflected is y-axis.
Following the statement established in the literature, we have:
The point (2, -9) when reflected over the y-axis, the x-coordinate is assumed to be the additive inverse, thus the new co-ordinate is (-2, -9).
The new point is (-2, -9).
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Find the value of each variable
Answer:
Step-by-step explanation:
since they are verticle angles:
8x+7=9x-4
subtract 8x and add 4
x=11
Write an equation in point-slope form for the line through the two points. Then change it toslope-intercept form. Rewrite the equation in standard form.10. (1, 2) and (3, 12)11. (6, 2) and (-2,-2) 12. (4,1) and (1,4)Please help I have sooo many assignments (:
For the point 13. we have that the line passes through the points (-1,-2) and (0,1) then the slope is
[tex]m=\frac{-2-1}{-1-0}=\frac{-3}{-1}=3[/tex]and the line equation will be:
[tex]y-1=3x\Rightarrow y=3x+1[/tex]For the point 14: we have that the line passes through the points (-1,0) and (0,-1) then the sslope is:
[tex]m=\frac{-1-0}{0-(-1)}=\frac{-1}{1}=-1[/tex]and the line equation will be:
[tex]y=-1(x-(-1))\Rightarrow y=-x-1[/tex]For the point 15: the line equation is y=-3 because the y coordinate will be always the same (-3) and the slope of the line will be equal to zero
3.21. a causal lti system has the following system function:(2(a) what is the roc for h(z)? (b) determine if the system is stable or not. (e) determine the difference equation that is satisfied by the input x[n) and the output yin. (d) use a partial fraction expansion to determine the impulse response h[n].
The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge.
What is meant by the roc for h(z)?When applying the z-transform on the sequence h, the ROC concept is applied to the function H(z) (n). The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge. Neither X(z), the input, nor Y(z), the output, are involved in the ROC.
The region (regions) where the z-transform converges is known as the region of convergence (ROC). We can uniquely determine the inverse z-transform thanks to ROC. Let's first think about some examples. The unit sample δ(n)has z-transform 1 , hence ROC exists all the z plane .
The Registrar of Companies assigns the company registration number, or CIN number as it is known in India (ROC). The Ministry of Corporate Affairs oversees the ROC, which is present in several Indian states. It is utilized to locate the essential information for every firm that is registered in India.
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Please help simple math 50 points
Answer:
2 pizzas
Step-by-step explanation:
5 7/8 - 4 1/16=
5 14/16 - 4 1/16 ==> make the denominators equal to each other so they can be easily subtracted in the next step
5 + 14/16 - (4 + 1/16)=
5 + 14/16 - 4 - 1/16 =
5 - 4 + 14/16 - 1/16 =
1 + 13/16 = 1 13/16 which is approximately 2 pizzas
Solve the compound inequality. 2x-4 > 8 or 3x-1 < -10
-3 < x < 6
x > 6 or x < -3
x > 2 or x < -3
x < 6 or x < -3
The solution to the compound inequality is x > 6 or x < -3
How to solve compound inequality?An inequality is a mathematical expression that has <, >, ≤ and ≥.
A compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
add 4 to both sides of the inequality
2x - 4 + 4 > 8 + 4
2x > 12
divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
add 1 to both sides of the inequality
3x - 1 + 1 < - 10 + 1
3x < - 9
divide both sides by 3
x < -9 / 3
x < -3
Therefore, x > 6 or x < -3
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The solution to the compound inequality will be; x > 6 or x < -3
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two functions in an problem.
A compound inequality is defined as an inequality that combines two simple inequalities.
Therefore, solve the compound inequality that will be;
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
Then add 4 to both sides of the inequality so,
2x - 4 + 4 > 8 + 4
2x > 12
Now, divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
Again, add 1 to both sides;
3x - 1 + 1 < - 10 + 1
3x < - 9
Then divide both sides by 3;
x < -9 / 3
x < -3
Therefore, solution to the compound inequality is; x > 6 or x < -3
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You are planning to place a bet on your local sports team, the red sparrows. the sparrow's have a past record of 4-5 (4 wins, 5 losses) at this venue. however you also know that their record is 2-7 in games where it rains and it has rained at 60% of their games this season. 4 if the red sparrows win their game what is the probability that it rained at that game?
The probability that it rained at that game is 0.49.
Probability is the the ratio of a particular event with total number of event. It tells the possibility that an event can occur.
Probability that it rains P(R) = 0.60
probability that it won't rain P(R') = 1-0.60
= 0.4
Red sparrows have a past record of 4 wins and 5 loses when it does not rain, that is
P( winning/R') = 4/9 (win% = 4/total that is 5+4 which is 9)
P( lose/R') = 5/9 (lose % = 5/total)
When it rain the past record is 2 wins and 7 loses
P( win/R ) = 2/9
P( lose/R ) = 7/9
P (win) = P(R)*P(win/R) + P(R')*P(win/R')
= 4/9*0.4 + 2/9*0.6
If red sparrows win, then the probability that it rained at game
P (R/win) = P ( R η win) / P (win)
= 0.49
Therefore, we can conclude that the the probability that it rained at that game is 0.49.
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I inserted a picture because it was too much to type but please, if you answer try and do it fast. It's homework.
Jaleel and Angela purchased a bag of sugar and used it evenly so the amount of flour that they each need, based on their brownie recipes are:
Angela - 5 cups of flour Jaleel - 6 ²/₃ cups of flourHow to find the amount of flour needed?Jaleel and Angela purchased a 20-cup bag of sugar and divided it evenly which means that they each get 10 cups of sugar.
The number of cups of sugar needed per cup of flour is:
= Change in sugar / Change in flour
= (3 - 1.5) / (2 - 1)
= 1.5 cups of sugar
The amount of flour needed would be:
= Number of cups of sugar / Cups of sugar per cup of flour
= 10 / 1.5
= 6 ²/₃ cups of flour
Angela's recipe shows that the cups of sugar needed per cup of flour is:
= (2 - 0) / (1 - 0)
= 2 cups of sugar
This means that with 10 cups of sugar, the amount of flour needed is:
= 10 x 1/2
= 5 cups of flour
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like terms and distributive propertysimplify each expression by using the distributive property and by combining like terms
Given the expression:
[tex]\frac{1}{2}(12x-8)-\frac{1}{3}(18x-12)[/tex]using the distributive property we get the following:
[tex]\begin{gathered} \frac{1}{2}(12x-8)-\frac{1}{3}(18x-12)+ \\ \frac{1}{2}(12x)+\frac{1}{2}(-8)-\frac{1}{3}(18x)-\frac{1}{3}(-12)= \\ 6x-4-6x+4=0 \end{gathered}[/tex]therefore, the simplified expression is 0
3. Find the equation of a line passing through (5,-6) parallel to : x + 3y = 8
The general slope intercept form is : y = m * x + b
Where m is the slope and b is y - intercept
Given the equation of the line : x + 3y = 8
Write the equation in slope intercept form to find the slope of the line
so, solve for y :
[tex]\begin{gathered} x+3y=8 \\ 3y=-x+8 \\ \\ y=-\frac{1}{3}x+\frac{8}{3} \end{gathered}[/tex]So, the slope of the given line = -1/3
The parallel lines have the same slope
so, the slope of the required line = -1/3
And the equation will be :
[tex]y=-\frac{1}{3}x+b[/tex]Find the value of b using the given point ( 5 , -6 )
When x = 5 , y = -6
[tex]\begin{gathered} -6=-\frac{1}{3}\cdot5+b \\ -6=-\frac{5}{3}+b \\ -6+\frac{5}{3}=b \\ \\ b=-\frac{13}{3} \end{gathered}[/tex]So, the equation of the line will be :
[tex]y=-\frac{1}{3}x-\frac{13}{3}[/tex]it can be written as : 3y = -x - 13
[tex]x+3y=-13[/tex]a survey of over 7{,}0007,0007, comma, 000 randomly selected employees in 151515 nations recently showed that employees who work in a digital workplace tended to be happier than those who don't work in a digital workplace. can we conclude that working in a digital workplace caused employees to be happier? why?
We cannot conclude that working in a digital workplace caused employees to be happier from the survey.
How is the conclusion from the survey explained?
A survey is a technique for acquiring data which could be considered as an information and not be considered as a conclusion.Surveys are statistical tools which are insufficient to generalize the entire population.A formal questionnaire is developed, and the questions are then asked in a specific order, according to the structured method of data gathering used in surveys , which doesn't include any scientific research or proof.Experimental research is not conducted in surveys which include only descriptive research.Scientific evidences from experiments are required to conclude that working in a digital workplace caused employees to be happier.To learn more about surveys, refer:
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A) What percentage of the cars are black?
B) 7 out of 12 black cars are new,express this value as a percentage rounding to two
decimal places.
C) What fraction of the cars were red?
D) Express the number of red cars as a percentage rounding to two decimal places?
Step-by-step explanation:
The total number of cars=24
Number of black cars=12
Divide 12 by 24,multiplied by 100%
12÷24 ×100=50%
Therefore, 50% of the cars are black
Find the mean of the data in the dot plot below.
Answer:
There is no dot plot below
Step-by-step explanation:
Mimi wants to spend a $25 gift card on two kinds of in -app purchases for her favorite game: premium skins that cost $2.99, and tools that cost $4.99.
The equation that shows the way that Mimi can spend a $25 is 2.99p + 4.99t = 25.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the premium skins be p.
Let the number of tools be t.
This will be illustrated as:
(2.99 × p) + (4.99 × t) = 25
2.99p + 4.99t = 25
This illustrates the equation.
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Mimi wants to spend a $25 gift card on two kinds of in -app purchases for her favorite game: premium skins that cost $2.99, and tools that cost $4.99. What is the equation to depict this?
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³ = 20b³
2. (3a²) ² x 2 (b ²) ³ = 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] 5d
3. 15d ³ divided by 3d ² = 5d
What is Operations?
An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's acuity is determined by the number of operands.
The given problems are:
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³
= 4 x 5b³
= 20b³
2. (3a²) ² x 2 (b ²) ³
By the exponent rule:
[tex](x^{n} )^m[/tex] = [tex]x^{n * m}[/tex]
= [tex]x^{nm}[/tex]
∴ 3[tex]a^{2*2}[/tex] x 2[tex]b^{2*3}[/tex]
= 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex]
3. 15d ³ divided by 3d ²
15d ³ ÷ 3d ²
By the exponent rule:
[tex]a^{m}[/tex]÷[tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
∴ 5[tex]d^{3-2}[/tex] = 5[tex]d^{1}[/tex]
= 5d
Hence, The solutions are 20b³, 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] and 5d
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9. Determine whether the following graph is a function or a relation.
Answer: Relation
Step-by-step explanation: it is a relation because if you take any number on the x axis and look at its points there are two points on multiple parts
eli needs to order some new supplies for the restaurant where he works. .Therestaurant needs at least 546 knives. There are currently 312 knives. If each set on
sale contains 10 knives, write and solve an inequality which can be used to determine
x, the number of sets of knives Eli could buy for the restaurant to have enough
knives.
Eli could buy is at least 24 sets of knives
How to determine the number of sets of knives Eli could buy?From the question, we have the following parameters:
Number of knives needed = At least 546Number of knives in the restaurant = 312Number of knives per set = 10Let the number of sets be x
So, we have the following representations
Number of knives needed = Number of knives needed + Number of knives per set x Number of set
So, we have
312 + 10x ≥ 546
Evaluate the like terms
10x ≥ 234
Divide by 10
x ≥ 23.4
Rewrite as
x ≥ 24
Hence, the number of sets of knives Eli could buy is at least 24
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Answer:
Inequality: 312+10x≥546
x≥24
Step-by-step explanation:
its the same as the bottom
