Answer:
[tex]\fbox {all real numbers}[/tex]
Step-by-step explanation:
7x + 8 = 1/6 (42x + 48)
7x + 8 = 7x + 8
x = all real numbers
A coin tossed 5 times. What is the probability of getting
i) All heads?
ii) All tails?
iii) Exactly 2 heads
iv) Exactly 3 tails
v) Exactly 1 head
vi) At least two heads
umm....... I think it was exactly 2 head
50 children had a choice of beans,plantain and rice.21 of them took beans,24 took plantain and 18 took rice.3 took beans only and 2 took rice only and 9 took plantain only. 5 took all the three items of food required. A.Draw a venn diagram to illustrate this information. B.Use your diagram to find the number of children who took ,1.plantain and beans only. 2.Rice and beans only.3.none of the three items of food.
The Venn diagram to illustrate this information is given in the image attached.
What is the Venn diagram about?The number of children who took plantain and beans only are:
Let beans = a
Rice = b
Plantain = P
So: a + b = 24 - 9 - 5 = 10
Note that 24 children took plantain.
9 children took only Plantain.
5 took the 3 food items.
So:
b + c = 18 -2 - 5 = 11
a + c = 21 - 3 - 5 = 13
P∩B = a + 5
= 6 + 5 = 11
R ∩ B = C + 5
=7 + 5 = 12
None of the three items of food =
50 - (3 + 2 + 9 + 6 + 4 + 7 + 5)
= 50 - 36
=14
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Find the slope of the line
Answer:
3/2
Step-by-step explanation:
comparing the straight line with ax + bx + c = 0,
we get a = 3 and b = -2
we know,
slope of line = -a/b
= -3/-2
= 3/2
Hope it helped
Which polynomial represents the sum below?
(4x²+1)+(4x² + x + 2)
A. 16x²+x+2
B. 8x²+x+2
C. 16x²+x+3
D. 8x²+x+3
Answer: D. 8x² + x + 3
Sum means the answer to an addition problem. To find the sum of polynomials, we will add like terms.
What are like terms?Like terms can be combined using addition or subtraction and have the same variables. Constants are also like terms with each other because they have no variables.
Solve(4x² + 1) + (4x² + x + 2) Starting equation from the question
= 4x² + 1 + 4x² + x + 2 Remove brackets
= 4x² + 4x² + x + 1 + 2 Rearrange to group like terms together
= 8x² + x + 1 + 2 Add like terms with the same 'x²' variables
= 8x² + x + 3 Add like terms that are constants
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Which is the graph of f(x) = 100(0.7)?
I assume you meant [tex]f(x)=100(0.7)^{x}[/tex]. The graph is shown in the image below.
Answer:
Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
Step-by-step explanation:
Edge
Multiply.
0.311
x 4.2
OA. 0.1866
OB. 1.3062
OC. 13.062
OD. 186.6
Answer: 1.3062
Step-by-step explanation:
0.311 * 4.2 = 1.3062
What is the solution of the quadratic equation (4y-3)^2=72
Answer:
To solve this quadratic equation, take the square root of both sides.
Since the left side is a perfect square, it will just be reduced to:
4y - 3
For the constant on the right side, the positive and negative roots must be considered.
√72 = ±6√2
Equating the two:
4y - 3 = ±6√2
4y = 3 ± 6√2
y = (3 ± 6√2)/4
y = (3 + 6√2) / 4 = 2.87
and
y = (3 - 6√2) / 4 = -1.37
GUYS PLEASE HELP WITH THIS PLEASE
Examine how sounds of music are related to trigonometric functions.
What does change of amplitude do? How about frequency?
Using graphs and equations, represent multiple transformations explaining their relevancy to the sound wave
The sounds of music are related to trigonometric functions because trigonometry is used in measuring the level of the pitch of a sound wave or musical note.
How is trigonometry used in sound?It should be noted trigonometry is important for measuring pitch level. The notes are measured in Hertz.
A sound wave's amplitude relates to the change in the pressure that's caused by the wave measured at a specific location.
The sound is perceived as louder when the amplitude increases.
Pieces of music often have repetitive choruses or bars, similar to patterns. In mathematics, we look for patterns to interpret and predict the unknown. Music uses the same techniques. If you look at a piece of music, artists look at the notes they see to find the rare (high or low) and uncommon notes.
In this way, the notes are related. Relationships are important in mathematics and create an interesting link between music and mathematics.
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A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than two percentage points
Answer:
The number of computers that must be surveyed is 1681.
Step-by-step explanation:
The formula to find the sample size is given by:-
[tex]n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}[/tex]
where p = prior population proportion,
[tex]\frac{z_{\alpha }}{2}[/tex]= Two-tailed z-value for ∝
E= Margin of error.
As per the given, we have
Confidence level :
1 - ∝ = 0.90
⇒∝= 1 - 0.90= 0.10
Two -tailed z-value for ∝= 0.10 : [tex]\frac{z_{\alpha }}{2}[/tex] = 1.64
E= 2%=0.02
We assume that nothing is known about the percentage of computers with new operating systems.
Let us take p=0.5 [we take p= 0.5 if the prior estimate of proportion is unknown.]
The required sample size will be:-
[tex]n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}[/tex]
=> [tex]0.25(82)^{2}[/tex]
=> 1681
Hence, the number of the computer must be surveyed = 1681
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The volume of a cone of height 4cm is 48cm². Find the radius (take π=22/7)
Answer:
22
Step-by-step explanation:
Is easy just multiple
A basket contains 3 oranges and 3 mangoes. A playful baby picks two fruits at random from this basket. If X denotes the number of oranges thus picked, determine the probability distribution of X
There are [tex]\binom62=15[/tex] ways of selecting any two fruit from the basket, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
If the baby picks out [tex]k[/tex] oranges, where [tex]k\in\{0,1,2\}[/tex], it can do so in
[tex]\dbinom 3k \dbinom3{2-k} = \dfrac{3!}{k!} \dfrac{3!}{(2-k)! (1 + k)!}[/tex]
ways.
Then the PMF (probability mass function) of [tex]X[/tex] is
[tex]P(X=x) = \begin{cases} \dfrac{\binom30 \binom32}{\binom62} = \dfrac3{15} & \text{if }x=0 \\\\ \dfrac{\binom31 \binom31}{\binom62} = \dfrac9{15} & \text{if }x = 1 \\\\ \dfrac{\binom32 \binom30}{\binom62} = \dfrac3{15} & \text{if }x=2 \\\\ 0 &\text{otherwise}\end{cases}[/tex]
In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8.
Triangle D F E is shown. Line segment G H is drawn from side D F to side E F to form triangle G F H. The length of D G is 15, the length of G F is 5, the length of E H is 12, and the length of D E is 8.
To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that
To prove that △DFE ~ △GFH by the SSS similarity theorem, the correct answer is; Option C: HF is 4 units and GH is 2 units
How to prove the similarity theorem?The SSS Similarity theorem states that two triangles are similar If all the three sides of one of the triangles are in same proportion to the three sides of the other triangle.
Since triangle DFE is similar to triangle GHF as seen in the attached diagram, then we can say that;
DF/GF = DE/GH
20/5 = 8/GH
GH = 2 units
Also:
EF/HF = DF/GF
(12 + HF)/HF = 20/5
HF = 4 units
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Please answer all 3 questions I will give brainliest if I can if ur right!
Answer:
1. 30 ft
2. sqrt(2164) yd
3: 12 cm
Step-by-step explanation:
For all three questions I'll be using the Pythagorean Theorem which states that a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the base and height
Question 1:
40^2 + d^2 = 50^2
1600 + d^2 = 2500
d^2 = 900
d = 30
Question 2:
42^2 + 20^2 = c^2
2,164 = c^2
c = sqrt(2164)
Question 3:
5^2 + a^2 = 13^2
25 + a^2 = 169
a^2 = 144
a = 12
Of all awarded prizes, 10% are worth $1000, 20% are worth $100, and 70% are worth $10. Find the expected winnings if you purchase a single ticke
Answer:
$127
Step-by-step explanation:
[tex](.10 \times 1000) + (.20 \times 100) + (.70 \times 10) = 100 + 20 + 7 = 127[/tex]
Help help needed for composition of function
Answer:
[tex]\circledast \ \ f\circ f\left( x\right) = x[/tex]
[tex]\circledast \ \ g\circ g\left( x\right) =4x - 21[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{5}{2x}[/tex]
g(x) = 2x - 7
==============
[tex]f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }[/tex]
[tex]=\frac{5}{2\left( \frac{5}{2x} \right) }[/tex]
[tex]=\frac{5}{\left( \frac{5}{x} \right) }[/tex]
[tex]=5\times\frac{x}{5}[/tex]
[tex]=x[/tex]
_____________
[tex]g\circ g\left( x\right) =2(g(x)) - 7[/tex]
= 2(2x - 7) - 7
= 4x - 14 - 7
= 4x - 23
(6.03)
What is the constant term in the expression 6x³y + 8x² + 5x + 7? (Input a numeric value only.)
Numerical Answers Expected!
Answer for Blank 1:
Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard. (the answer is 10 points but can someone please tell me how to do it and pls explain why)
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Account earns 8.5% interest. If you invest $6,609 now how much interest will you earn in 5years
Answer:
simple interest is $281(nearest whole number)
Step-by-step explanation:
S. I=PXTXR
100
P=$6609
T=5
R=8.5 or 85/10
S. I=6609X5X85
100X10
=280.8825
=281
An avid traveler is investigating whether travel websites differ in their pricing. She chooses a random sample of 32 hotel rooms from across the state and notes the price of each room from site A and site B. The mean difference (site A – site B) in the prices for the rooms is $5.49 with a standard deviation of $18.65.
Assuming the conditions for inference have been met, is there evidence that the prices of hotel rooms from site A and site B are different, on average? Use a significance level of a = 0.05.
A. Because the P-value is less than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
B. Because the P-value is greater than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
C. Because the P-value is less than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.
D. Because the P-value is greater than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.
you loaned a friend $100 and will charge him 5% annual simple interest when he pay it back
The amount of interest after 3 years will be $15.
The complete question is given below.
You loaned a friend $100 and will charge him 5% annual simple interest when he pay it back. What is the amount of interest after 3 years?
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The interest is given as
I = (P × R × T) / 100
Where, P is the initial amount, R is simple interest rate, and T is the time.
We have
P = $100
R = 5%
T = 3 years
Then the interest will be
I = (100 × 5 × 3) / 100
I = $15
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If angle 1= 105°, angle 12= (3x + 15)°, and angle 7 = (8y-5)°, determine the values
of x and y?
The value of the variable x is 30° and the value of the variable y is 10°.
The missing diagram is attached below.
What is an angle?The angle is the distance between the intersecting lines or surfaces.
Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.
Vertically opposite angle – When two lines intersect, then their opposite angles are equal.
Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.
If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.
∠1 = ∠5 = ∠9 = 105° (corresponding angles)
∠1 = ∠4 = 105° (Vertical opposite angles)
∠1 + ∠2 = 180° (linear angle)
∠2 = 75°
∠2 = ∠3 = 75° (Vertical opposite angles)
∠3 = ∠8 = ∠12 = 75° (corresponding angles)
Then the value of x and y will be
∠9 = ∠12
∠1 = ∠12
105° = (3x + 15)°
3x = 90°
x = 30°
∠6 = ∠7
75° = (8y – 5)°
8y = 80°
y = 10°
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the polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity at x=-2.
find a possible formula for P(x)
P(x)=
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
Given the roots of the polynomial, therefore, the following details can be written as,
The polynomial has a root of multiplicity 2 at x=2, (x-2)²The polynomial has a root of multiplicity 2 at x=0, (x-0)²The polynomial has a root of multiplicity 1 at x=-2, (x+2)¹Therefore, the polynomial will become,
P(x) = (x-2)²(x-0)²(x+2)¹
= (x²+4-4x) (x)² (x+2)
= (x²+4-4x) (x³+2x²)
= x⁵ + 2x⁴ + 4x³ + 8x² - 4x⁴ -8x³
= x⁵ - 2x⁴ - 4x³ + 8x²
Hence, the possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².
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Find the slope of the line passing through the points (-5, -3) and (0, -4).
Answer:
To find the slope:
[tex]\frac{(y_{1} - y_{2})}{(x_{1} - x_{2})} =\frac{(-3-(-4))}{(-5-0)} =\frac{1}{-5}[/tex]
Hope it helps!
In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F. The highest monthly average temperature occurs in July at 78 °F. Write and graph a sinusoidal curve equation to model the average monthly temperature in Michigan. Assume the period is 12 months and that January is at the origin of the graph of this function. (6 points)
ANSWER ATTACHED
sinusoidal curve equation 29 sin ([tex]\pi[/tex]/9 x)-49
What is Equation of a sinusoidal curve ?Given the graph of a sinusoidal function, we can write its equation in the form y = A·sin(B(x - C)) + D using the following steps. D: To find D, take the average of a local maximum and minimum of the sinusoid. y=D is the "midline," or the line around which the sinusoid is centered.
In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F.
The highest monthly average temperature occurs in July at 78 °F
Assume the period is 12 months and January is at the origin of the graph of this function.
sinusoidal curve equation that models the data y
Then, Graph the curve using x = 0 for January, and x = 11 for December, so that x = 12 will be the start of the next year, or end of the period.
So, using the property of sinusoidal curve equation we have
=29 sin ([tex]\pi[/tex]/9 x)-49
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What to do when forget the pasword to the account?
Answer:
usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"
Which of the following transformations produce congruent figures?
i. Rotation
ii. Reflection
iii. Translation
iv. Dilation
i, ii, and iii
i and ii
iv only
iii and iv
pls help how do i solve for x in this equation??
Answer:
x = -2
Step-by-step explanation:
1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2
What is the approximate area of the shaded sector in the circle shown below
A.29.04 in^2
B.13.51 in^2
C.7.26 in^2
D.6.75^2
Answer:
please provide the diagram
Step-by-step explanation:
for the solution figure is necessary so provides us to solve this problem
A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder
with a height of 7 cm and a radius of 2 cm. The paper label is wrapped around the can and covers only
the side of the can (not the top or bottom). The company uses, on average, 3612.64 cm² of paper
each minute making these labels. How many labels does the company make, on average, each
minute?
For your calculations, do not round any intermediate steps, and use the button on a calculator. Round
your answer to the nearest hundredth.
The company needs 41 labels on average, each minute.
What is the circumference of a circle?The perimeter of a circle (circumference): 2 π radius
Replacing with the values given:
C = 2 (3.14) 2 = 12.56 cm
So, the area of one label is:
Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.
Now, the number of label be n
87.92 x n = 3612.64 cm2
n = 3612.64 / 87.92
n = 41.09
Hence, The company needs 41 labels on average, each minute.
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The graphs below have the same shapes. What is the equation for the red graph?
The equation for the red graph will be g(x) = x² + 3.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function f(x) is given below.
f(x) = x²
Then the function g(x) will be given as
g(x) = x² + 3
Then the equation for the red graph will be g(x) = x² + 3.
The missing graph is given below.
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