Answer:
Express each number in scientific notation.
1) 0.0056 = 5.6 × 10^-3
3) 4,085 = 4.085 × 10³
5) 0.000796 = 7.96 × 10^-4
Standard and Scientific Notations
50,413 = 5.0413 × 10^4
11 = 1.1 × 10^1
11 = 1.1 × 10^1
2) 24,010 = 2.401 × 10^4
4) 0.017 = 1.7 × 10^-2
6) 952 = 9.52 × 10^2
8) 0.004 = 4 × 10^-3
Use the graph to find the value of f (x) when x = 3 for the function f (x)=-x2-4.
Answer: (3,-13)
Step-by-step explanation:
[tex]f(x)=-x^2-4\\x=3[/tex]
math is hard ok
attachments below
The measurement that does not represent the dimension of the triangle is 15, 30 and 45cm
The measurement that does represent the dimension of the triangle is 4, 8 and 10 cm.
What are the measurements?Two triangles are similar if the ratio of the side lengths of the triangle are equal.
The ratio of the length of the triangles are 6 cm : 12 cm : 15 cm
Express the ratio in its simplest form - 2 cm : 4 cm : 5 cm
Ratio of 12, 24 cm and 30cm in its simplest form - 2 : 4 : 5
Ratio of 10, 20 and 25cm in its simplest form - 2 : 4 : 5
Ratio of 18, 36, 45cm in its simplest form - 2 : 4 : 5
Ratio of 15, 30 and 45cm in its simplest form - 1 : 2 : 3
Ratio of 4, 8 and 10 in its simplest form - 2 : 4 : 5
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12 divided by 11 in fraction form
Answer: if you are talking about mixed number form the answer is 1 1/11 the improper/exact form would just be twelve over eleven (12/11)
Step-by-step explanation:
Madison’s band used to practice for 50 minutes every Tuesday. Now they practice 130% as many minutes as they used to. How many minutes do they play on Tuesdays now?
Corey’s cat weighed 4 pounds. A year later, it weighed 175% of its previous weight
Answer: 65 min
7 pounds
Step-by-step explanation:
Use on of the equations:Bag Price ÷ Pounds in Bag = Cost/pound
Cost/pound x Pounds fed = Cost/day
Cost/day x # of Horses = Cost/head/day
Cost/head/day x # of days in month = Cost/head/month
1. You have 5 horses and you feed 4.5 pounds of grain to each in one day. What is the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag?
2. You have 32 heads of horses, and each gets 1.5 pounds of grain per feeding. You feed grain twice a day, once in the morning and once in the evening. If you feed grain that costs $13 per 50lb bag, then is the cost per head per month?
3. You have 12 heads of horses, and each gets 2.5 pounds of grain per feeding. You feed grain twice a day, once in the morning and once in the evening. If you feed grain that costs $13 per 50lb bag, then is the cost per head per month?
Solving the questions from the given equations
1)the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag is $16.2
2) The cost per head per month is $23.4
3) The cost per head per month is $39
What is Equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
1) The grains use feed for one horse = 4.5pound
The cost of 1 bag of grain = $27 per 50lb
The cost of 1lb grain = $0.54
Now the monthly cost of the grain will be:
Cost/head/day x # of days in month = Cost/head/month
$0.54 x 30 = $16.2
Hence, the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag is $16.2
2) The amount of grain use to feed for one head = 1.5pound
If the grain is feed twice a day = 1.5 x 2
= 3.0
The cost of the grain = $13 per 50lb
The cost of 1lb grain = 13 / 50
= $0.26
The cost of grain feed in one day = 0.26 x 3
= $0.78
The cost of per head per month =
0.78 x 30 = $23.4
Hence, The cost per head per month is $23.4
3)The amount of grain use to feed for one head = 2.5pound
If the grain is feed twice a day = 2.5 x 2
= 5pounds
The cost of the grain = $13 per 50lb
The cost of 1lb grain = 13 / 50
= $0.26
The cost of grain feed in one day = 0.26 x 5
= $1.3
The cost of per head per month =
1.3 x 30 = $39
Hence, The cost per head per month is $39
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Solve this system of equations by eliminating.
5x + 7y=3
-5x + 7y=-17
The value of x is 2 is and y is -1 is after solving equation by elimination method
what is linear equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
What is elimination method ?To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
5x + 7y=3 .....(i)
-5x + 7y=-17......(ii)
Solve equation ii and iii
-5x + 7y=-17
5x + 7y=3
14y = -14
y = -1
put the value of y in equation 1
5x + 7y=3
5x + 7(-1)=3
5x - 7 = 3
5x = 10
x =2
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Tyrone's bank account had a balance of -$72.04 last week. His paycheck of $335.67 was deposited this week. If there have been no
other transactions, which of the following is true?
OA. Tyrone's current account balance is $263.63.
is $263
OB. Tyrone's current account balance is
$263.63.
OC. Tyrone's current account balance is -$407.71.
OD. Tyrone's current account balance is $407.71.
Hello, the correct answer to the question should be [tex]263.63[/tex] dollars.
Tyrone does not have any money in his bank account. Also, his balance contains a negative symbol, which means that he owes money to the bank.
[tex]Balance=-72.04[/tex]When his paycheck arrives, money will come into his account. This means that Tyrone will pay off his debt to the bank.
[tex]335.67-(72.04)[/tex]Since the money coming into his account and his balance have different symbols, we will add the two values and get the result.
[tex]=263.63[/tex] dollars.can u answer this, its for homework. Thx!
It is to be noted that the distance between P and ρ is: [tex]\approx[/tex] 15.52
This solution is arrived at using the Line Segment theorem. See further explanation below.
What is the line segment theorem?The length of the line segment connecting two points in a plane is defined as the distance between two points. The method for calculating the distance between two locations is often written as
[tex]d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} [/tex]
Hence, since we have ρ is to contain two points, we will solve as follows:
Distance between ρ and P where ρ is (0, -3) and (7,4)
we have to multiply the coordinates.
To multiply coordinates, you have to multiply the corresponding values.
That is
[tex]x_{1} \times x_{1} [/tex]
and
[tex]y_{1} \times y_{1}[/tex]
In this case:
x1 = 0
[tex]x_{1} = 0[/tex]
also
[tex]x_{1} = 7[/tex]
[tex]y_{1} = - 3[/tex]
also
[tex]y_{1} = 4[/tex]
Hence, for
[tex]x_{1} = 0 \times 7 = 0[/tex]
for
[tex]y_{1} = - 3 \times 4 = 12[/tex]
Hence, solving for the distance between P and ρ, we'd use coordinates of P as = (4, 3); and coordinates of ρ as = (0, -12)
Recall that distance is given as
[tex]d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} [/tex]
Hence,
d = √((0-4)² + (-12-3))²)
[tex]d = \sqrt{{(( {0 - 4}^{2} }) + { (- 12 - 3)}^{2} } [/tex]
Expand the brackets
[tex]d = \sqrt{ { - 4}^{2} + ( { - 15}^{2} } )[/tex]
[tex]d = \sqrt{16 + 225} [/tex]
[tex]d = \sqrt{441} [/tex]
d = 15.5241746963
Approximately,
d = 15.52
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helppppppp meeee plsssssWhich construction could this be?Inscribed SquareInscribed HexagonInscribed RectangleInscribed Octagon
1) Judging by the picture, which resembles a construction done with a compass with the same distance, therefore we can tell a regular polygon.
2) We can also trace some line segments then we'll have a:
[tex]Inscribed\:Hexagon[/tex]
The formula for the area of the shaded
region on the diagram is:
Area of the circle - Area of the square
The area of the circle is 67.1 cm² rounded to
1 decimal place.
The area of the square is 12.3 cm² truncated
to 1 decimal place.
Write the error interval for the area, a, of the
shaded region
The error interval of the area a of the shaded region
What is Error Interval?
Error intervals are the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated.
Given,
Area of the circle = 67.1cm²
Area of the square = 12.3cm²
According to the question:
The formula for the area of the shaded
region on the diagram is:
Area of the circle - Area of the square
Putting the value of Area of circle and Area of square
= 67.1cm² - 12.3cm²
= 54.8cm²
The Error interval of area a = 54.8 + 0.5 and 54.8 - 0.5
= 54.85 and 54.75
Hence, Area of shaded region is 54.85< a < 54.75
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what is the value of x
Answer:
x = 70
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × 3 = 540°
sum the interior angles and equate to 540
x + 160 + 110 + 105 + 95 = 540
x + 470 = 540 ( subtract 470 from both sides )
x = 70
Help asap. 30 points
Answer:
The terms are rearranged, so the Commutative Property is correct.
The size P of a small herbivore population at time t (in years) obeys the function P(t) = 600e0.16t if they haveenough food and the predator population stays constant. After how many years will the population reach 3000?Round to the nearest hundredth.F) 10.06 yrG) 16,31 yrH) 48.65 yrD 19.86 yr
Given the function
[tex]P(t)=600e^{0.16t}[/tex]When P(t)=3000
[tex]\begin{gathered} P(t)=3000 \\ 600e^{0.16t}=3000 \end{gathered}[/tex][tex]\begin{gathered} \text{divide through by 600} \\ e^{0.16t}=\frac{3000}{600} \\ e^{0.16t}=5 \\ 0.16t=in5 \\ 0.16t=1.6094 \\ t=\frac{1.6094}{0.16} \\ t=10.05899yr \\ t=10.06yr(\text{nearest hundredth)} \end{gathered}[/tex]Hence, it will take 10.06yr for the population to reach 3000, option F
Environmentalists estimate an annual population decrease of giraffes in the wild of 3.5% due to development. This can be modeled by the function p(x) = 140,000(0.965)x, where x is the number of years of tracking the populations. Conservationists have developed a sanctuary that has shown the ability to increase the population by 0.85% per year. The increase can be modeled by the function S(p) = p(1.0085)x.
Which function represents S(p(x)), rounded to the nearest ten thousandth?
S(p(x)) = 135,100(0.9732)x
S(p(x)) = 135,100(1.9735)x
S(p(x)) = 140,000(0.9732)x
S(p(x)) = 140,000(1.9735)x
The equation of the function S(p(x)), rounded to the nearest ten thousandth is S(p(x)) = 140,000(0.9732)ˣ option (C) is corrrect.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation of the function:
p(x) = 140,000(0.965)ˣ
Which is the annual population decrease of giraffes in the wild of 3.5% due to development.
Plug x = 1.0085
[tex]\rm p(x) = 140,000(0.965)^{1.0085}[/tex]
S(p(x)) = 140,000(0.965)ˣ(1.0085)ˣ
S(p(x)) = 140,000(0.9732)ˣ
Thus, the equation of the function S(p(x)), rounded to the nearest ten thousandth is S(p(x)) = 140,000(0.9732)ˣ option (C) is corrrect.
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Gale sells 16 bags of cherries at the farmers market. Each bag weighs 1.8 pounds. How many pounds of cherries does Gale sell in all?
Number of bags= 16
Bag weight= 1.8 pounds
Then, number of pounds is
= 16x 1.8 = 28.8 pounds of cherries
what is (tan x + cot x) sin x * cos x ?
pls helppp
(tan x + cot x) sin x * cos x is 1
(tan x + cot x) sin x * cos x
= (tan x + 1 / tan x) sin x * cos x because cot x = 1 / tan x
= (((tan x) ^2 + 1) / tan x) sin x * cos x because (tan x) ^2 +1= (sec x) ^2
= (sin x / cos x) tan x
= tan x / tan x
= 1
Isabella draws a mystery number from a bag with various integers inside and then describes it to the class read the clues below and then Circle all of the integers that it could be
1. The opposite of the integer is positive
2. The absolute value of the integer is positive
3. The integer is not zero
-8
11
15
-21
An integer exists a whole number that can be positive, negative, or zero and is not a fraction.
What is meant by an integer?Unlike fractional numbers, integers can only be positive, negative, or zero. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. An integer is a whole number that can be positive, negative, or zero and is not a fraction.
Any number that exists a part of a collection of all the aforementioned number categories is considered an integer. Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
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This is question 13 from the book, on p. 436. The numbers are probably no longer accurate, but don't worry about that.) Show all five steps of the hypothesis test. You can either type them in here, or write them out on paper and send me a scan/picture of your work.The mean age of Senators in the 209th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At α = 0.05, is there sufficient evidence that state senators are on average younger than 60.35 (the average age Senators in Washington)?
Answer:
There is not sufficient evidence to support the conclusion that senators are average younger than 60.35
Step-by-step explanation:
Given a simple random sample, the size is 40 senators.
Since the relevant statistic is the sample mean, 60.35 years.
Calculate t as:
[tex]t=\frac{\bar{x}-\mu_{\bar{x}}}{\frac{s}{\sqrt[]{n}}}[/tex]*Significance level is 0.05.
[tex]\begin{gathered} t=\frac{60.35-55.4}{\frac{6.5}{\sqrt[]{40}}} \\ t=4.82 \end{gathered}[/tex]Area of 0.05, one-tail yields t=1.685.
Since t=4.82 does not fall in the critical region bounded, we fail to reject the null hypothesis.
There is not sufficient evidence to support the conclusion that senators are average younger than 60.35
use the trapezoidal rule, the midpoint rule, and simpson's rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.) 4 0 ln(3 ex) dx, n
a. Trapezoidal Rule- 9.413607
b. Midpoint Rule-9.393861
c. Simpson's Rule -9.400407
a. We use n=8 for this integral, .Δt=4-0/8=0.5
Therefore the integral range is[0,0.5,1.0,1.5......3.0,3.5....4.0 ]
#For the Trapezoidal Rule:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Tn=[/tex]Δr/2[∫([tex]x0[/tex])+2∫(x1)+....+∫(xn)]
=[tex]\int\limits^4_0[/tex][tex]In(2+ex[/tex])dx≈[tex]T8[/tex]
=0.5/2[[tex]In[/tex](2+[tex]e0.0[/tex])+2In(2+e0.5)+2In(2+e1.0)+....+2In(2+e3.5)+In(2+e4.0)]
=0.25[1.098612+2.588754+3.102889+3.737962+4.479090+5.304017+6.189846+7.117283+4.035976]
≈9.413607
Hence, the approximate integral value using Trapezoidal rule is 9.413607
b.For the Midpoint Rule, we calculate the integral as:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Mn=[/tex]Δx[∫[tex](x1)[/tex]+∫([tex]x2)[/tex]........∫([tex]xn)}[/tex]
x1 is the midpoint of the ith interval.
From our interval ,[0,0.5,1.0,1.5....3.0,3.5,4.0]the applicable intervals are
[0.25,0.75,1.25,2.25,2.75,3.25,3.75]
We therefore have the integral value as:
=4/8[[tex]In[/tex](2+[tex]e0.25[/tex])+In(2+[tex]e0.72[/tex])+In(2+[tex]e1.25[/tex])+....+In(2+[tex]e1.75[/tex])+In(2+[tex]e2.25[/tex])[tex]In[/tex](2.75)+In(2+e0.5)+In(2+e1.0)]
Hence, the approximate integral value using the Midpoint Rule is 9.393861
c. For the Simpson's Rule, we calculate the integral rule as follows:
Hence, the approximate integral value using the Simpson's Rule is 9.400407
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A particle is moving on the x-axis and the position of the particle at time t is given by x(t), whose graph is shown above. Which of the following is the best estimate for the speed of the particle at time t=4 ? Responses 0
The speed of the particle at time t=4 is 5 units.
We are given the x(t) vs time curve.
To find:
Speed of particle at t = 4
We know that the slope of x-t curve represents the speed of the particle.
To calculate the speed of the particle at t = 4, We will calculate the slope of the curve at t = 4
Slope = y₂ -y₁ / x₂ - x₁
Slope = 40 - 10 / 6 - 0
Slope = 30 /6
Slope = 5
From here we can say that the slope of the curve between x = 0 and x = 6 is equal to 5.
So the value of speed is also 5 units.
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The function g(x) = (x + 2)2 + 4 is a transformation of the parent function f(x) = x2. Which of the following statements are true? Select all that apply.
A. Function g is the result of f being translated right 2 units and down 4 units.
B. Function g is the result of f being translated left 2 units and up 4 units.
C. The graph of function f opens upward.
D. The graph of function f opens downward.
E. The graph of function f is compressed by a factor of 2.
Answer: B. Function g is the result of f being translated left 2 units and up 4 units. and C. The graph of function f opens upward.
Step-by-step explanation:
It is translated 2 units to the left and 4 units up because in the function of a(x-h)^2k, h represents the function going left of right and k representing the function going up and down. a represents it stretching if it is greater than 1 and compressing if less than 1 and if it is negative it reflects over the x axis however here nothing changed for the a so it did not stretch nor compress nor reflect over the x axis
compute the mean median mode * 63.373 Point 486.81 05.21 28.4 101.5 94.7 + 116.9
Mean = Sum of points/ number of points
Median
is 4 2/3 greater than 4 5/6
Answer:
4 [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Make them equivalent
4 [tex]\frac{2}{3}[/tex] if I multiply the numerator (top) and the denominator (bottom) by 2 I get
4[tex]\frac{4}{6}[/tex]
4 [tex]\frac{5}{6}[/tex] is greater than 4 [tex]\frac{4}{6}[/tex]
A blank is a whole number that has more than two factors
Answer:
A composite number is a whole number greater than 1 with more than two factors.
Step-by-step explanation:
Please use graph provided.
Graph the line with the slope of 4/3 and goes through the point (1,3)
The graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted
The slope of the line = 4/3
The line is passing through the point = (1,3)
Here we have to use the point slope form the line
The point slope form of the line = [tex](y-y_{1} )= m(x-x_{1})[/tex]
Where m is the slope of the line
[tex](x_{1},y_{1} )[/tex] is the coordinate of the point
Substitute the values in the equation
(y-3) = 4/3 (x-1)
y-3 = (4/3)x - 4/3
y = (4/3)x - 4/3 + 3
y = (4/3)x + 5/3
We got the slope intercept of the line.
Plot the graph using the slope intercept form of the line
Hence, the graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted
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∠c and ​∠d​ are vertical angles with m∠c=−3x 58 and m∠d=x−2. what is m∠d? enter your answer in the box. ​ °
D has a value of 13 using vertical angles.
What is a vertical angle?
When two lines intersect, the angles that face each other are called vertical angles.Instead of referring to them as being up-down, "vertical" in this context denotes that they share a vertex (corner point).Assuming that C and D constitute vertical angles
The formula is C = (-3x) + 58 and D = x - 2.
We must ascertain what D's measurement is.
Vertical angles are really a pair of opposing angles created when two lines cross.
A and B in the figure represent vertical angles. C and D are also.
Angles vertically are always congruent. Accordingly, in this illustration, A, B, and C, D
Therefore, value of C = D (-3x)+ 58 = x – 2
By assembling,
(-3x )- x = (-2) - 58
By doing more math, 4x = 60 (-4x = - 60)
4 x = 60/4 x = 15 when both sides are divided.
So, ∠D = (x - 2) and
= 15 - 2
So, ∠D = (x - 2) and
Consequently, D has a value of 13 using vertical angles.
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using long division
helo me please show your complete ssolutions
Step-by-step explanation:
Make the facts and then you can get the answer easily
The radius of the wheel of a unicycle is 14 inches. What is the
distance, in inches, that the unicycle covers after 10 full
rotations of the wheel? Use 3.14 for pi
Step-by-step explanation:
We need to find the circumference of the equation.
One circle circumference is a circle full rotation.
[tex]c = \pi(d)[/tex]
[tex]d = 2r[/tex]
[tex]c = 2r\pi[/tex]
R is 14.
[tex]c = 28\pi[/tex]
We need a rotation 10times so
[tex]10 \times 28\pi = 280\pi[/tex]
Find the value of k, if x – 1 is a factor of p(x)
i) (i) p(x) = x^2+x+k
Answer:
k = -2.
Step-by-step explanation:
By the Factor Theorem, if x - 1 is a factor then p(1) = 0.
So, p(1) = (1)^2 + 1 + k = 0
k = -1 - 1
k = -2.
Use the scatter plot to answer the question.
A scatter plot with points at (negative 16, negative 7), (negative 9, negative 5), (negative 3, negative 3), (1, 2), (5, 4), (8, 3) & (14, 6).
Which function best fits the data in the scatter plot?
f(x)=2x−3f of x is equal to 2 x minus 3
f(x)=2x+1f of x is equal to 2 x plus 1
f(x)=12x−3f of x is equal to 1 half x minus 3
f(x)=12x+1
Using linear regression, the function that best fits the data in the scatter-plot is given by:
f(x) = 1/2x + 1.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the context of the problem.
The scatter-plot in this problem contains these following points:
(-16, -7), (-9, -5), (-3, -3), (1, 2), (5, 4), (8, 3) and (14,6).
Inserting these points into a calculator, the equation is given by:
f(x) = 0.46835x + 1.
Approximating the slope to 1/2 considering the given options, the function is given by:
f(x) = 1/2x + 1.
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