Answer:
0.315 to nearest thousandth.
Step-by-step explanation:
7e^3x − 4 = 14
7e3x = 18
e^3x = 18/7
3x = ln(18/7)
x = ln(18/7) / 3
= 0.31482.
What are the quotient and remainder of (3x4 - 2x + 7x-4)= (x - 3)?
a. 3x2 + 772 +21x + 70; 206
c. 3x4 + 7%? +21x2 + 70; 206
b. 3x + 77? + 21x + 70; -206
d. 37° +73+ + 21x + 703 76
The quotient of dividing (3x⁴ - 2x³ + 7x² - 4) by (x - 3) is 3x³ + 7x² + 28x + 84 and the remainder is 248
How to determine the quotient and the remainder?The division expression is given as:
(3x⁴ - 2x³ + 7x² - 4) / (x - 3)
Set the divisor to 0
x - 3 = 0
Solve for x
x = 3
Substitute x = 3 in 3x⁴ - 2x³ + 7x² - 4
3x⁴ - 2x³ + 7x² - 4 = 3(3)⁴ - 2(3)³ + 7(3)² - 4
Evaluate
3x⁴ - 2x³ + 7x² - 4 = 248
This means that the remainder is 248
Recall that:
Dividend = Divisor * Quotient + Remainder
So, we have:
3x⁴ - 2x³ + 7x² - 4 = x - 3 * Q + 248
Subtract 248 from both sides
3x⁴ - 2x³ + 7x² - 252 = x - 3 * Q
Divide both sides by x - 3
Q = (3x⁴ - 2x³ + 7x² - 252)/(x - 3)
Factorize the numerator
Q = (x - 3)(3x³ + 7x² + 28x + 84)/(x - 3)
Cancel out the common factors
Q = 3x³ + 7x² + 28x + 84
Hence, the quotient is 3x³ + 7x² + 28x + 84 and the remainder is 248
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Which of the following are based on empirical probability
The empirical probability is Life insurance, Car insurance, and Mortality.
What is empirical probability?
The ratio of the number of outcomes in which a defined event occurs to the total number of trials, not in a theoretical sample space but in a real experiment, is the empirical probability, relative frequency, or experimental probability of an event.
Therefore the empirical probability will be Life insurance, Car insurance, and Mortality.
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Find the height of the tree below to the nearest foot.
why are asymptotes important in rational function graphs
Answer:
when sketching the curves of functions.
Step-by-step explanation:
There is a wide range of graph that contain asymptotes and that includes rational functions, hyperbolic functions, tangent curves, and more. Asymptotes are important guides when sketching the curves of functions. This is why it’s important that we know the properties, general forms, and graphs of each of these asymptotes.
How many values are in the range 0 to 55
There are 55 values in the range 0 to 55
How to determine the number of values?The minimum is given as:
Minimum = 0
The maximum is given as:
Maximum = 55
The range is calculated using:
Range = Maximum - Minimum
So, we have:
Range = 55 - 0
Evaluate
Range = 55
Hence, there are 55 values in the range 0 to 55
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This composite figure is made up of three simpler shapes. What is the area of the figure? 7 cm 4 cm 5 cm 4 CE 8 cm A. 66 square cm R 50 square cm C. 46 square cm D. 80 square cm
The total area of the given figure will be 66 square cm.
What is an area?
The space occupied by any two-dimensional figure in a plane is called the area. Here we have three shapes a triangle, a rectangle and a parallelogram.
Total area = Area of triangle + Area of rectangle + Area of parallelogram
Total area = [(1/2) x 4 x7] + [4 x 5] + [ 4 x 8 ]
Total area = 14+20+32
Total area = 66 square cm
Hence the total area of the given figure will be 66 square cm.
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Noa hopes to pick the winning ticket during her math class’s raffle. The student who picks the ticket with a true statement will win. Which is the winning ticket?
A correct answer is an option a which is 2x = - 23
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
We need to select correct statements from the given options.
2 ( x - 6 ) = - 35
2 x - 12 = - 35
2x=-35+12
2x = - 23
Therefore, 2 ( x - 6 ) = - 35 is equivalent to .2x=-23
8(x-7)=35
8x-556=35
8x=91
Therefore, 8(x-7)=35 is not equivalent to 8x=91.
9(x-6)=-35
9x-54=-35
9x=19
Therefore,9(x-6)=-35 is not equivalent to 9x=19.
4(x-5)=35
4x-20=35
4x=55
Therefore,4(x-5)=35 is not equivalent 4x=55 to .
Hence, the correct answer is an option a which is 2x = - 23
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I need help pls
What is the value of x?
Answer:
30
Step-by-step explanation:
the value of x, bring the variable to the left side and bring all the remaining values to the right side
Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher’s hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean μ = 92.12 mph and a standard deviation of σ = 2.43 mph.
Compute the z-score of pitch with speed 95.8 mph. (Round your answer to two decimal places.)
Approximately what fraction of these four-seam fastballs would you expect to have speeds between 91 mph and 93.2 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)
Approximately what fraction of these four-seam fastballs would you expect to have speeds below 91 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)
A baseball fan wishes to identify the four-seam fastballs among the fastest 20% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 20%? (Round your answer to the nearest 0.1 mph.)
a box is 10 inches long, 3 inches wide, and 4 inches high. what is the surface area in square inches of the closed box
Answer: 164 square inches
Step-by-step explanation:
[tex]2(10 \cdot 3+10 \cdot 4+3\cdot 4)=164[/tex]
Select the expression that is equivalent to the given expression: 3(x + 2) - x
A: 5x + 6
B: 2x + 6
C: 2x + 2
D: 9
Answer:
B
Step-by-step explanation:
if you simply 3(x+2)-x, you get 2x+6.
it is not 3x+6 because x already equals 1. 2x+6=2x+6
Rachel has a large pond on her property. The pond contains many different kinds of fish including bass.
The inequalities that can be used to determine the possible number of bass in the pond over time are: P≥250e^0.048t; P≤275e^0.048t.
Given:
r=4.8/100=0.048
Initial amount:
Lower end=250
Upper end=275
Using this equation to determine the inequalities
A=p×e^rt
Where:
A=Amount
P=Population
r=Growth rate
t=Time
Let plug in the formula
Inequalities:
P≥250e^0.048t
P≤275e^0.048t
Therefore the inequalities are : P≥250e^0.048t; P≤275e^0.048t.
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Which description matches the algebraic expression 45 n?
the sum of a number and 45
the quotient of a number and 45
the product of a number and 45
the difference of a number and 45
Answer:
The product of a number and 45
Step-by-step explanation:
Answer:
the product of a number and 45
Step-by-step explanation:
i just finished the quiz
if x=3,y=-2(negative 2) and z=6,what is 7xyz
Step-by-step explanation:
x = 3
y = - 2
z = 6
Question:[tex]7xyz[/tex]
Solution,
= 7 × 3 ( - 2 ) × 6
= 21 ( - 2 ) × 6
= - 42 × 6
= - 252
hence the answer is - 252....
What is the length of the segment joining the points at (-6, 8) and (6, 3)?
Enter your answer in the box.
units
Answer:
13 units
Step-by-step explanation:
So the length of those 2 points is 6+6 = 12.
The height would be 8-3 =5
Using pythagoras, you can find out the length of the line joining the 2 points so:
[tex]5^2 + 12^2 = 169[/tex]
[tex]\sqrt{169} = 13[/tex] units
If ∠1 and ∠2 are vertical angles and m∠1 = 108°, find m∠2.
Answer:
[tex]m\angle 2= 108^{\circ}[/tex]
Step-by-step explanation:
Vertical angles are equal.
Answer:
108°
Step-by-step explanation:
vertical angles are angles opposite each other when two lines cross.
if <1 and <2 are vertical angles, it means that m<1 = m<2
m<1= 108°
therefore, m<2= 108°
Alex has 64 cubes with dimensions in ft like
1/2 x 1/2 x 1/2
He uses all the cubes to fill a box shaped like a larger rectangular prism. There are no gaps.
What is the volume in cubic ft of the larger rectangular prism?
Choose the graph that represents the equation y = –|x + 4| + 1.
Answer:
It's the last choice.
Step-by-step explanation:
It has a V shape because of the absolute value lines | |
But it is an inverted V because of the leading negative.
The vertex is at y = 1 because of the + 1.
The + 4 moves the whole graph 4 units to the left of the origin.
So the vertex is at (-4, 1)
Answer:
The correct option is graph D. because the equation has all negative x values, meaning this graph will be to the left.
Why is the graph not facing upwards?
This is because some of the y values are equal to 1 or negative 1, causing the graph to face downwards.
A car travels along a hill inclined at 10 degrees with the ground and travels 900 feet. What is the horizontal distance travelled by the car, to the nearest tenths of a foot.
Answer:
886.3 feet
Step-by-step explanation:
cos(10°) = d/900
d = 900 cos(10°) = 886.3 feet
The distance around a triangle is 40 centimeters. If two sides are equal and the length of the third side is 10 centimeters, what is the length of each of the other two sides?
Answer:
15 centimeters each = the two other sides of the triangle is 30 cm.
Step-by-step explanation:
What is the value of x?
We have been given the two lengths as x and y So, the value of x would be equal to root 80.
How to obtain real measurements from the ratio of two measurements?Suppose the real measurements were "a" and "b"
Then their ratio will be formed as
[tex]\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}[/tex]
where is a common factor (not 1)
This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly canceled from both the numerator and the denominator.
Thus, a = px, b = qx
we have been given the two lengths as x and y.
From the figure, we know that
11: y = y: 5
Express in fraction
11/y = y / 5
y^2 = 5(11)
y ^2 = 55
So, y = √55
From Pythagoras theorem;
[tex]x^{2} =5^{2} +y^{2} \\\\x^{2} =5^{2} +55 \\\\x^{2} =25 + 55\\\\x^{2} =80\\\\x = \sqrt{80}[/tex]
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Use the formula pH = log (1/H*) to find the pH of the substance given its concentration
of hydrogen ions in a liter of acid rain that has a pH. Round your answer to the nearest
ten-thousandth.
10. pH = 3.6
A rectangle is 13 feet long and 4 feet wide. Find its area.
A 48 square feet
B
17 square feet
52 square feet
D 47 square feet
Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answer:
w = 23
Step-by-step explanation:
so the total degree of a triangle is 180,
when you add all 3 it should equal 180.
35 + (5w) + (w + 7) = 180
subtract 35 from both sides, 35 - 35 + (5w) + (w + 7) = 180 - 35
(5w) + (w + 7) = 145
combine like terms (add the w's), (5w + w) + 7 = 145
6w + 7 = 145
subtract 7 from both sides, 6w + 7 - 7 = 145 - 7
6w = 138
divided both sides by 6 to get w alone, 6w / 6 = 138 / 6
w = 23
These two shapes have the same perimeter.
regular hexagon
square
Not actual size
The length of each side of the hexagon is 8 centimetres.
Calculate the area of the square.
Question
Answer: u can use this to practice and u can also find your awnser in thes pic
Step-by-step explanation:
I need this answer asap please
Answer:283 awnser is 283
Step-by-step explanation:
2 2/3 + 1/5
Could Someone Help??
Answer:
13/15
Step-by-step explanation:
you multiply the numbers by each other like 3×1/5 = 3/15 and 5×2/3 = 10/15
then you add them to get 13/15
wants to wrap a shipping box shaped like a rectangular prism. The box is 30 inches tall and has a square base with sides that each measure 3 inches. How much paper will she use?
Answer:
360
Step-by-step explanation:
uh if the box has a square base of 3 inches and a square has 4 sides then 3x4=12 and then multiply by 12x30= 360
Answer:
Answer:
360
Step-by-step explanation:
uh if the box has a square base of 3 inches and a square has 4 sides then 3x4=12 and then multiply by 12x30= 360
Step-by-step explanation:
can someone help me rn?
Answer:
y = 1
Step-by-step explanation:
Given:
equation of the parabola: [tex]y=a(x-1)^2+q[/tex]points on the parabola: (-1, -9) and (1, 1)Substitute point (1, 1) into the given equation of the parabola to find q:
[tex]\begin{aligned}\textsf{At}\:(1,1)\implies a(1-1)^2+q &=1\\a(0)^2+q &=1\\q &=1\end{aligned}[/tex]
Substitute the found value of q and point (-1, -9) into the given equation of the parabola to find a:
[tex]\begin{aligned}\textsf{At}\:(-1,-9)\implies a(-1-1)^2+1 &=-9\\a(-2)^2+1 &=-9\\4a+1 &=-9\\4a &=-10\\a &=-\dfrac{5}{2}\end{aligned}[/tex]
Therefore, the equation of the parabola is:
[tex]y=-\dfrac{5}{2}(x-1)^2+1[/tex]
The maximum or minimum point on a parabola is the vertex.
Vertex form of a parabola: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex.
Therefore, the vertex of the parabola is (1, 1) and so the maximum value of y = 1
Vertex at (1,q)
There is a point already given from which parabola passes through its (1,1)
So q=1Hence
vertex=(1,1)Equation:-
y=a(x-h)²+ky=a(x-1)²+1Now put (-1,-9)
-9=a(-2)²+1-9=4a+14a=-10a=-5/2a is negative hence parabola is opening downwards
So
vertex is maximum
Max value
y=1At Pizza Pi, 12% of the pizzas made last week had extra cheese. If 3 pizzas had extra cheese, how many pizzas in all were made last week?