One fourth of m minus six is equal to two times the sum of m and 9:
[tex]\dfrac{1}{4}m -6=2(m+9)[/tex]This is self-explanatory, please comment if something is unclear.
Question 2Drew has 50 marbles; red, green and blue.
Equation for this:
r + g + b = 50He has six more red marbles than blue marbles:
Equation for this:
r = b + 6He has four fewer green marbles than blue marbles:
Equation for this:
g = b - 4Substitute r and g into first equation and solve for b:
r + g + b = 50b + 6 + b - 4 + b = 503b + 2 = 503b = 48b = 48/3b = 16Drew has 16 blue marbles.
Find the length of the radius of a circle with a center at –7 2i and a point on the circle at 33 11i.
The length of the radius of a circle exists 41 units.
How to estimate the length of the radius of a circle?
Given: The center exists at -7+2i and a point in the circle at 33+11i.
The radius of the circle exists given by the following formula;
The radius of the circle [tex]$=\sqrt{x^{2}+y^{2}}$[/tex]
The center exists at -7 + 2i and a point in the circle at 33 + 11i.
[tex]$&x(33-(-7)), y(2 \mathrm{i}-11 \mathrm{i}) \\[/tex]
simplifying the equation, we get
[tex]$&\mathrm{x}(33+7), \mathrm{y}(-9 \mathrm{i}) \\[/tex]
[tex]$&\mathrm{x}(40), \mathrm{y}(-9(-1)) \\[/tex]
[tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex]
The center of the circle exists at [tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex].
The length of the radius of a circle exists,
Radius [tex]$}=\sqrt{x^{2}+y^{2}} \\[/tex]
substituting the values of x and y, we get
Radius[tex]$}=\sqrt{40^{2}+9^{2}} \\[/tex]
Radius [tex]$}=\sqrt{1600+81} \\[/tex]
Radius [tex]$=\sqrt{1681} \\[/tex]
Radius = 41 unit
Therefore, the length of the radius of a circle exists 41 unit.
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Line segment st is dilated to create line segment s't' using the dilation rule dq,2.25. point q is the center of dilation. line segment s t is dilated to create line segment s prime t prime. the length of q t is 1.2 and the length of q s is 2. the length of s s prime is x and the length of t t prime is 1.5. what is x, the distance between points s' and s?
The distance between points S' and S is 2.5 units.
What is proportionality theorem in triangles?If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.
Given that,
line segment ST is dilated to create line segment S'T' using the dilation rule DQ.
Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5 units, SS' = x units.
We need to find the value of x, the distance between points S' and S.
Since the line ST is dilated to S'T' with center of dilation Q, so the triangles STQ and S'T'Q must be similar.
We know that the corresponding sides of two similar triangles are proportional.
So, from ΔSTQ and ΔS'T'Q, we get
[tex]\frac{SQ}{S'Q} =\frac{TQ}{T'Q}[/tex]
[tex]\frac{SQ}{SQ+S'S} =\frac{TQ}{TQ+T'Q}[/tex]
[tex]\frac{2}{2+x} =\frac{1.2}{1.2+1.5}[/tex]
[tex]\frac{2}{2+x} =\frac{1.2}{2.7}[/tex]
[tex]\frac{2}{2+x} =\frac{12}{27}[/tex]
[tex]\frac{1}{2+x} =\frac{6}{27}[/tex]
12+6x = 27
6x = 15
x = 2.5
Hence, Thus, the required value of x is 2.5 units.
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Please help and explain.
Answer:
B
Step-by-step explanation:
It's B
Answer:
Option B
Step-by-step explanation:
The equation is:
[tex]y=10-2x[/tex]
when x=2
[tex]y=10-2(2)010-4=6[/tex]
When x = 3
[tex]y=10-2(3)=10-6=4[/tex]
When x=4
[tex]y=10-2(4)=10-8=2[/tex]
Hope this helps
What is a31 of the
arithmetic sequence for
which a5 = 12.4 and
ag = : 22.4?
The value of a₃₁ of the arithmetic sequence exists 77.4.
How to find the value of a₃₁ of the arithmetic sequence?Given: a₅ = 12.4 and a₉ = : 22.4
For the arithmetic sequence a₁, a₂, a₃, ..., the n-th term exists
where d = common difference
a₅ = 12.4,
a₁ + 4d = 12.4 .........(1)
Because a₉ = 22.4,
a₁ + 8d = 22.4 .........(2)
Subtract (1) from (2), we get
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Dividing throughout by 4, we get
d = 2.5
From (1), we get
a₁ = 12.4 - 4 [tex]*[/tex] 2.5 = 2.4
a₃₁ = 2.4 + 30 [tex]*[/tex] 2.5 = 77.4
Therefore, the correct answer is a₃₁ = 77.4
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A function of random variables used to estimate a parameter of a distribution is a/an _____.
A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.
What are the parameters of a random variable?A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.
An unbiased estimator exists in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply indicates that an unbiased estimator catches the true population value of the parameter on average, this exists because the mean of its sampling distribution exists the truth.
Also, we comprehend that the bias of an estimator (b) that estimates a parameter (p) exists given by; E(b) - p
Therefore, an unbiased estimator exists as an estimator that contains an expected value that exists equivalent to the parameter i.e the value of its bias exists equivalent to zero.
Generally, in statistical analysis, the sample mean exists as an unbiased estimator of the population mean while the sample variance exists as an unbiased estimator of the population variance.
Therefore, the correct answer is an unbiased estimator.
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Find the quotient.
18.)97.2
Answer:
540
Step-by-step explanation:
540 =18% of 97.2
Done please
it's quotient it's a synthax error..
Joel wanted his mom to buy a super-sized box of his favorite cereal, but his mom didn't think it would fit in her cupboard. The box had a volume of 6900 cm3, and the base was 23, the depth, 10. How high was it?
The height of the box would be = 30cm.
How to calculate the height of the box from the given volume?The volume of the box = 6900 cm3
The base of the box = 23 cm
The depth of the box = 10cm
Therefore the height of the box can be gotten from the formula used to calculate the volume of the box. That is;
Volume = base×depth×height
6900 = 23×10×h
make h the subject of formula;
height = 6900/230
= 30cm
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50 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 31 pupils use the swimming pool. 28 pupils use the gym. 7 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.
Using it's concept, it is found that there is a 0.3 = 30% probability to select a pupil that uses the swimming pool but not the gym.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 50 - 7 = 43 pupils use at least one of the pool or the gym.
We use the following relation, considering the numbers of each:
Both = Pool + Gym - At least one
Hence:
Both = 31 + 28 - 43 = 16.
From this, we have that out of 50 pupils, there are 31 - 16 = 15 pupils who use the pool but not the gym, hence the probability is:
p = 15/50 = 0.3 = 30%.
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Figure A is a scalr image of figur B. Figure A maps to Figure B with scale factor of 2/3. what is tge value of x?
Answer:
7
Step-by-step explanation:
You take the corresponding side that you know which is 10.5 and you multiply that by your scale factor of 2/3.
Another name for 10.5 is 10 [tex]\frac{1}{2}[/tex] and that can be changed to [tex]\frac{21}{2}[/tex]
([tex]\frac{21}{2}[/tex])([tex]\frac{2}{3}[/tex]) The two's cancel out and we are left with [tex]\frac{21}{3}[/tex] Which is the same as 7.
How many cars can be washed with 1 gallon of soap if 100oz Can
wash 11 cars?
Answer: 14 cars.
Step-by-step explanation:
A car can be washed with : 100/11 oz.
1 gallon=128 oz.
Hence,
[tex]\displaystyle\\\frac{128}{\frac{100}{11} } =\frac{128*11}{100} =\frac{1408}{100} =14,08\ (cars).[/tex]
The total number of cars that can be washed with 1 gallon of soap if 100oz Can wash 11 cars would be given as 14 cars
How to solve for the total numberTo determine how many cars can be washed with 1 gallon of soap, we need to find the ratio between the amount of soap used and the number of cars washed.
Given that 100 oz of soap can wash 11 cars, we can set up the following proportion:
100 oz soap / 11 cars = 1 gallon soap / x cars
I gallon is given as 128 OZ
Such that we have
128 x 100 / 11
= 14.08 cars
Hence the total number of cars would be given as 14 cars
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The store has a 30% discount on every item in stock. how much is the 5% sales tax reduced on an item that regularly sells for $10?
i need help on this question
For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
How much money should we pay in sales tax?
In this question we must determine the amount of money needed to pay in taxes by the purchase of an item with a discount. Sales taxes are an example of indirect taxes, this kind of indirect tax is usually calculated on the basis of total costs, including discounts. The amount of money need for the sales tax is described below:
t = (r / 100) · (1 - d / 100) · c (1)
Where:
d - Discount rater - Sales tax ratec - Item pricet - Sales tax totalIf we know that d = 30, r = 5 and c = 10, then the sales tax total is:
t = (5/ 100) · (1 - 30 / 100) · 10
t = 0.35
For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
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help me with this.
Calculate angles in a triangle
Step-by-step explanation:
Total Angle in a triangle is 180°
so D = 140 + 25 = 165°
D = 190° - 165° = 15°
Your answer is 15°.
Answer:
angle d = [tex]\boxed{15}^ {\circ}[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠d + 25° + 140° = 180°
⇒ ∠d + 165° = 180°
⇒ ∠d = 180° - 165°
⇒ ∠d = 15°
No matter what the value of s, 1s? is equal to the
value of s.
The complete statement is no matter what the value of s, √s² is equal to the absolute value of s?
How to complete the blank?The statement is given as:
No matter what the value of s, √s² is equal to the ______ value of s?
The above statement can be split as follows:
No matter what the value of s, √s² is equal to the ______ value of s?This means that, irrespective of the value of s, what would be the value of the square root of the square of s.
Assume that s is negative (say s = -2), the value of the square root of the square of s would be
√s² = √(-2)²
Evaluate the square
√s² = √4
Evaluate the square root
√s² = 2
See that s = 2 is the positive equivalent or absolute value of s = -2
Now, assume that s is positive (say s = 4), the value of the square root of the square of s would be
√s² = √4²
Evaluate the square
√s² = √16
Evaluate the square root
√s² = 4
See that s = 4 is the positive equivalent or absolute value of s = 4
Hence, the complete statement is no matter what the value of s, √s² is equal to the absolute value of s?
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Complete question
No matter what the value of s, √s² is equal to the ______ value of s?
A construction worker is pouring concrete stairs. The first step requires 1.7 cubic feet of concrete, and the first 4 steps require a total of 17 cubic feet. If the steps follow an arithmetic series, how much concrete is required for the first 12 steps
Based on the given parameters of a = 1.7 cubic feet and concrete for first 4 steps as 17 cubic feet, the concrete is required for the first 12 steps is 132.6 cubic feet
Arithmetic progressionFirst term, a = 1.7 cubic feetSum of first four terms = 17 cubic feetSn = n/2 {2a + (n - 1) d}
17 = 4/2{2×1.7 + (4 - 1)d}
17 = 2{3.4 + (3)d}
17 = 2(3.4 + 3d)
17 = 6.8 + 6d
17 - 6.8 = 6d
10.2 = 6d
d = 10.2/6
Common difference, d = 1.7Concrete required for first 12 steps;
Sn = n/2 {2a + (n - 1) d}
= 12/2{2×1.7 + (12-1)1.7}
= 6{3.4 + (11) 1.7}
= 6(3.4 + 18.7)
= 6(22.1)
= 132.6
Concrete required for first 12 steps = 132.6 cubic feet
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Answer:
132.6 cubic feet
Step-by-step explanation:
exponential growth and decay real-world word problems
The examples of exponential growth include bacteria population growth and compound interest and a real life example of exponential decay is radioactive decay.
What is exponential growth?Exponential growth is the pattern of data that shows sharper increases over time. Savings accounts with a compounding interest rate can show exponential growth.
There are many real-life examples of exponential decay. An example, is thatsuppose that the population of a city was 100,000 in 1980. Then every year after that, the population has decreased by 3% as a result of heavy pollution. This is an example of exponential decay.
One of the best examples of exponential growth is the observed in bacteria. It takes bacteria roughly an hour to be able to reproduce through prokaryotic fission. In this case, if we placed 100 bacteria in an environment and recorded the population size each hour, we would observe an exponential growth.
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Victor spent 1/2 of his salary on rent, 1/4 of the remainder on food and saved \mbox{Sh 1500). How much was his salary?
Nag basa nito walang jõwa
Tina wrote a check for $35 on Monday. On Tuesday she made of withdrawal of $60 and on
Wednesday she deposited $75. What is the change in Tina's account after the three days?
The change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25
Deposit and withdrawalDeposit is a sum of money or other asset given as an initial payment, to show good faith, or to reserve something for purchase.
Withdrawal on the other hand, is to extract money from an account.
Check = $35Withdrawal = $60Deposit = $75Change in Tina's account after the three days = - 35 - 60 + 75
= -95 + 75
= $-20
Therefore, the change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25.
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QP=
Help please thanks so much
Answer:
QP = | a - d |
Step-by-step explanation:
since the y- coordinates of P and Q are equal , both b
then PQ is the absolute value of the difference of the x- coordinates, that is
QP = | a - d | = | d - a |
Suppose you are building a storage box of volume 4368in^3. the length of the box will be 24 in. the height of the box will be 1 in. more than its width. find the height and the width of the box.
Answer:
height: 14 incheswidth: 13 inchesStep-by-step explanation:
The volume formula can be used to find the height and width of a box with volume 4368 in³ and height 1 in greater than width.
SetupThe volume formula is ...
V = LWH
Substituting given information, using w for the width, we have ...
4368 = (24)(w)(w+1)
SolutionWe want to find the value of w.
182 = w² +w . . . . . . . . divide by 24
182.25 = w² +w +0.25 = (w +0.5)² . . . . . . add 0.25 to complete the square
13.5 = w +0.5 . . . . . . . . take the positive square root
w = 13 . . . . . . . . . . . . subtract 0.5
h = w+1 = 14
The height of the box is 14 inches; the width is 13 inches.
__
Additional comment
By "completing the square", we can arrive at the exact dimensions of the box, as we did above. Note that we only added 0.25 to the equation to do this.
For numbers close together, the geometric mean (root of their product) is about the same as the arithmetic mean (half the sum):
[tex]\sqrt{w(w+1)}\approx\dfrac{w+(w+1)}{2}=w+\dfrac{1}{2}\\\\w\approx\sqrt{182}-\dfrac{1}{2}\approx12.99[/tex]
Using this approximation to arrive at the conclusion w=13 saves the steps of figuring the value necessary to complete the square, then adding that before taking the root.
Estimate √50 to the hundredths place.
Answer:
7.07
Step-by-step explanation:
Answer:
7.07
Step-by-step explanation:
Hello!
Let's find two perfect square numbers that are directly before and after 50.
[tex]\sqrt{49} < \sqrt{50} < \sqrt{64}[/tex][tex]7 < \sqrt{50} < 8[/tex]Since the square of 7 is the closest, we can use that as our whole number.
To find the decimal...49 is 1 away from 50, and 64 is 14 away. Rewriting it as a fraction and we get [tex]\frac{1}{14}[/tex]. The decimal is 0.07142857142.
Now, put 7 and 0.07142857142 together and we get 7.07142857142. Rounding that, we get 7.07.
The real value of Root 50 is 7.071067811865475, so the decimals were really close.
graph: g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2
[tex]g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2[/tex]
generate by: Amplitude:5 Period:4
Phase shift:(3 to the right) Vertical shift:-2
x=3,g(x)= 3
x=4,g(x)= -2
x=5,g(x)= -5
x=6,g(x)= -2
x=7,g(x)= 3
the graph is like cos(x)
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A regular octagon has side lengths of 8 centimeters. what is the approximate area of the octagon?
Answer:309
Step-by-step explanation:
Write an expression containing x2-terms, x-terms and constants. The
x2-terms should combine to −2x2 the x-terms should sum to 3x,
and the constants should sum to 3.
[tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
Like terms are terms whose variables (and their exponents such as the 2 in [tex]x^{2}[/tex]) are the same. Like terms can easily be added and substracted. Such questions just need like terms to be bought together and simplified
Infinite number of equations or expressions can be written for the given question. So writing one possibility for the given question,
= [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex]
which sums up to
= [tex]-2x^{2} +3x+3[/tex]
Thus [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
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If p(x) = x² - 1 and g(x)= 5(x-1), which expression is equivalent to (p - q)(x)?
A.5(x-1)-x²-1
B.(5x-1)-(x² - 1)
C.(x²-1)-5(x - 1)
D.(x²-1)-5x - 1
The expression which is equivalent to the required expression (p - q)(x) is; Choice C; (x²-1)-5(x - 1).
Which expression is equivalent to (p - q)(x) given that p(x) = x² - 1 and g(x)= 5(x-1)?It follows from the task content that the premise functions as given in the task content are;
p(x) = x² - 1
g(x)= 5(x-1).
Consequently, the required expression for the function operations; (p - q)(x) is simply;
p(x) - q(x) and is equivalent to;
(x² - 1) - 5(x - 1)
Therefore, the expression which is equivalent to the required expression (p - q)(x) is Choice C; (x²-1)-5(x - 1).
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HELP PLS WHAT IS X
Darn
Answer:
x = 55°
Step-by-step explanation:
x , 35° , 90° lie on a straight line and sum to 180° , that is
x + 35° + 90° = 180°
x + 125° = 180° ( subtract 125° from both sides )
x = 55°
Can someone help me please?
A.1/5
B.7/10
C.3/10
D.1/2
Using it's concept, the probability that a student plays basketball or soccer is given as follows:
B. 7/10.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
P(A or B) is the probability that a student plays basketball or soccer, hence, from the Venn diagram:
7 students play at least one of the sports, which are: Fran, Juan, Ian, Ella, Mickey, Mai and Marcus.There is a total of 10 students, which are the 7 that plays at least one of the sports, plus Karl, Jada and Gabby.Hence the probability P(A or B), that is, the probability that a student plays basketball or soccer, is given as follows:
p = 7/10.
Which means that option B is correct.
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A boat heading out to sea starts out at Point A, at a horizontal distance of 1315 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 12^{\circ}. At some later time, the crew measures the angle of elevation from point B to be 8^{\circ}. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Bearing is a topic that deals with distance and measure of the angle in locating the position of an object. The distance required in the question is 692 feet.
Bearing is a topic that relates the distance and measure of an angle so as to determine the accurate position of a given object. The angle with respect to the object is measured clockwise with respect to the North pole.
From the first part of the question, the height of the lighthouse, h, can be determined by applying the trigonometric function. So that;
Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
Tan 12 = [tex]\frac{h}{1315}[/tex]
h = Tan 12 x 1315
= 279.51
Thus the height of the lighthouse is approximately 280 feet.
Thus, let the distance between points A and B be represented by l. This implies that the distance from point B to the lighthouse is (l + 1315) ft.
So that;
Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
Tan 8 = [tex]\frac{280}{(l+1315)}[/tex]
Tan 8 x (l + 1315) = 280
0.141l + 185.415 = 280
0.141 l = 280 - 185.415
= 97.585
l = [tex]\frac{97.585}{0.141}[/tex]
= 692.092
l = 692 feet
Therefore, the distance between points A and B is 692 feet.
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What is the area of the triangle shown below?
Answer: the area of the triangle is 5.
Step-by-step explanation:
[tex]A(0;0) \ \ \ \ B(1;3) \ \ \ \ C(4;2) \ \ \ \ S_{ABC}=?\\Use \ the\ formula:\\\displaystyle\\\boxed{S=\frac{1}{2}*|[(x_A-x_C)*(y_B-y_C)-(x_B-x_C)*(y_A-y_c)] |}\\x_A=0\ \ \ \ x_B=1\ \ \ \ x_C=4\ \ \ \ y_A=0\ \ \ \ \ y_B=3\ \ \ \ \ y_C=2.\\S=\frac{1}{2}*|[(0-4)*(3-2)-(1-4)*(0-2)]|\\S=\frac{1}{2}*| [(-4)*1-(-3)*(-2)]|=\\ S=\frac{1}{2}*| (-4-6)|\\S=\frac{1}{2}*|(-10)|\\S= \frac{1}{2} *10\\S=5.[/tex]
What is the slope?
What is the slope?
What is the slope?
What is the slope?
What is the slope?
Answer:
okay it's name is Muhammad Deco alfansia ( ◜‿◝ )
Answer:
Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting.
Step-by-step explanation: Hope this helps you!
suppose sin(A)=-0.78. use the trig identity sin^2(A)+cos^2(A)=1 and the trig identity tan(A) = sin(A)/cos(A) to find tan(A) in quadrant IV. round to the ten-thousandth.
a. -0.2039
b. 1.3941
c. 0.8671
d. -1.2464
In quadrant IV, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258[/tex]
Then by the definition of tangent,
[tex]\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}[/tex]