Answer:
B.2152
Step-by-step explanation:
To solve this we are using the standard exponential growth equation:
[tex]y=a(1+b)^x[/tex]
where
[tex]y[/tex] is the final value after [tex]x[/tex] years
[tex]a[/tex] is the initial value
[tex]b[/tex] is the growing rate in decimal form
[tex]x[/tex] is the time in years
We know from our problem that the GNP is growing 4.8% per year, so [tex]b=\frac{4.8}{100} =0.048[/tex]. We also know that the GDP in 1994 was $5.9 billion and the desired GNP is $10 trillion, so [tex]a=5,900,000,000[/tex] and [tex]y=10,000,000,000,000[/tex].
Replacing values
[tex]y=a(1+b)^x[/tex]
[tex]10,000,000,000,000=5,900,000,000(1+0.048)^x[/tex]
[tex]10,000,000,000,000=5,900,000,000(1.048)^x[/tex]
Divide both sides by 5,900,000,000:
[tex]\frac{10,000,000,000,000}{5,900,000,000} =(1.048)^x[/tex]
Take natural logarithm to both sides
[tex]ln(1.048)^x=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]
[tex]xln(1.048)=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]
Divide both sides by ln(1.048)
[tex]x=\frac{ln(\frac{10,000,000,000,000}{5,900,000,000})}{ln(1.048)}[/tex]
[tex]x[/tex] ≈ 158
We now know that Canada's GNP will reach $10 trillion after 158 years from 1994, so to find the year we just need to add 158 years to 1994:
1994 + 158 = 2512
We can conclude that the correct answer is B.2152
Plz help me with this
Answer: Equivalent
Step-by-step explanation:
[tex]y=-\dfrac{1}{3}x+\dfrac{2}{3}\\\\\text{Multiply by 3 to clear the denominator: }3y = -x + 2\\\text{Add x to both sides: }x+3y=2\\\text{Multiply both sides by 2: }2x+6y=4[/tex]
When given a system of equations, the definitions of the solution are:
Consistent & Independent: exactly ONE solution (lines intersect)Consistent & Dependent: INFINITE solutions (same line)Inconsistent: NO solutions (parallel lines)In the given system, the equations are the same which means they have INFINITE solutions --> The system is Consistent & Dependent = Equivalent.
What is the factorization of 729^15+1000?
Answer:
The factorization of [tex]729x^{15} +1000[/tex] is [tex](9x^{5} +10)(81x^{10} -90x^{5} +100)[/tex]
Step-by-step explanation:
This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form [tex](a^{3} +b^{3} )[/tex] or [tex](a^{3} -b^{3})[/tex]. It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of [tex]729x^{15} +1000[/tex] by using the sum and difference of cubes factorization.
1.) We calculate the cubic root of each term in the equation [tex]729x^{15} +1000[/tex], and the exponent of the letter x is divided by 3.
[tex]\sqrt[3]{729x^{15}} =9x^{5}[/tex]
[tex]1000=10^{3}[/tex] then [tex]\sqrt[3]{10^{3}} =10[/tex]
So, we got that
[tex]729x^{15} +1000=(9x^{5})^{3} + (10)^{3}[/tex] which has the form of [tex](a^{3} +b^{3} )[/tex] which means is a sum of cubes.
Sum of cubes
[tex](a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})[/tex]
with [tex]a= 9x^{5}[/tex] y [tex]b=10[/tex]
2.) Solving the sum of cubes.
[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )[/tex]
[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)[/tex]
.
What does that sign mean? What’s the name?
Pie. It’s pie 3.14.... the name of that sign is pie
Answer:
That symbol represents pi.
Step-by-step explanation:
Pi is used by mathematicians to represent the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. Hope this helps!
For a group experiment, your science class measured the fine-particulate concentrations in the air at random places around campus, and estimated a sample average of 22 μg/m3 (micrograms per cubic meter). If 144 readings were taken, and the standard deviation of the sample measurements was 4 μg/m3, you are 99.7% confident that actual concentration of fine particulates at the school is
Answer:
The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).
Step-by-step explanation:
Given : Sample size(n)= 144
Sample mean [tex]\mu= 22 ug/m^3[/tex]
Standard deviation [tex]\sigma=3.5 ug/m^3[/tex]
To find : 99.7% confident that actual concentration of fine particulates at the school is?
Solution :
The formula for confidence interval is
[tex]CI=\mu \pm z\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Substituting the values in the formula,
[tex]CI=22 \pm 3\times\dfrac{3.5}{\sqrt{144}}[/tex]
[tex]CI=22 \pm 3\times\dfrac{3.5}{12}[/tex]
[tex]CI=22 \pm 3\times 0.2916[/tex]
[tex]CI=22 \pm 0.8748[/tex]
[tex]CI=22+0.8748, 22-0.8748[/tex]
[tex]CI=22.8748, 21.1252[/tex]
Therefore, The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).
Answer:
21 ug/m^3 - 23 ug/m^3
Step-by-step explanation:
Just got it right
-2a(a+b-5)+3(-5a+2b)+b(6a+b-8) the coefficient of the a^2 term is
Answer:
-2
Step-by-step explanation:
the coefficient is the number in front of the variable.
Pls find the answers
Answer:
the number of sheet available is 75, 000
you take the total number of pages available = 8 x 75,000
= 600,000 pages
then each notebooks contains 200 pages
= 600,000 / 200
= 3000 notebooks can be made
Step-by-step explanation:
Answer:
3000 notebooks
Step-by-step explanation:
75,000*8=600000
600000/200=3000
in 2000 the world's population was 6.08 billion and was increasing at a rate 1.21 each year. use the function to predict the population in the year 2020
Answer:
the population would be 30.28 billion by 2020
Step-by-step explanation:
y=6.08 + 1.21x
y = 6.08 + 1.21(20)
y = 6.08 + 24.2
y = 30.28
I NEED HELP ASAP!
What's the area of this Trapezoid?
Answer:
Area of Trapezoid is 88 Units^2
Step-by-step explanation:
Area of trapezoid = (a+b)/2 * h
where a and b are lengths of each base and h is the height of trapezoid.
In the question given:
a= 17 (because a is the upper base and value will be 17)
b= 27 (because b is the lower base and value will be 17+5+5 = 27)
h= 4
Area of trapezoid = (a+b)/2 * h
= (17 +27)/ 2 * 4
= 22 * 4
= 88 Units^2
Area of Trapezoid is 88 Units^2
Find the system determinant of the given matrix. -30 -6 6 30
Answer:
- 864
Step-by-step explanation:
In the case of a 2 × 2 matrix the determinant may be defined as:
|A| = [tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]= ad-bc
Given in the question a matrix
[tex]\left[\begin{array}{cc}-30&-6\\6&30\\\end{array}\right][/tex]
(-30)(30) - (-6)(6)
-900 + 36
- 864
Answer:
Option A: -30
For Odyssey
**If you are on the pre-test then you might wanna take your time because they can suspect if you are cheating**
A game has 15 balls for each of the letters B, I, N, G, and O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I . 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability?
A. I
B. N
C. G
D. O
Theoretically, each letter should have the same probability of occurring since there are 15 of each. There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability [tex]\dfrac{15}{75}=\dfrac15[/tex] of being drawn.
This means one would expect a theoretical frequency of [tex]\dfrac{1250}5=250[/tex], i.e. any given letter should get drawn 250 times, which means the answer is D.
Answer:
252 D-O
Step-by-step explanation:
250 and theoretically 252
9) Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 14
10) Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
-10 and 8
The distance between two points on a number line is found using the absolute value of their difference. For instance, the distance between 2 and 14 is 12 units, and the distance between -10 and 8 is 18 units.
Explanation:The concept of absolute value is crucial when determining the distance between two points on a number line. This distance is represented by the difference in their values, disregarding which one is larger or whether they are positive or negative.
Example 9: Finding the Distance Between 2 and 14The expression for the distance is |2 - 14|. Evaluating this, we find |2 - 14| = |-12| = 12. Therefore, the distance between the numbers 2 and 14 on the number line is 12 units.
Example 10: Finding the Distance Between -10 and 8The expression for the distance is |-10 - 8|. Evaluating this, we find |-10 - 8| = |-18| = 18. Therefore, the distance between the numbers -10 and 8 on the number line is 18 units.
Plz help me with this
Answer: b) -5 ≤ y ≤ 1
Step-by-step explanation:
y = 3 cos (4x) - 2
↓ ↓
amplitude vertical shift
The amplitude is 3 which gives a range of -3 to 3 but there is also a shift down of 2 units so the new range is: -3 - 2 = -5 to 3 - 2 = 1
-5 ≤ y ≤ 1
Solve the equation for y
2x+5y=5
***Plz Help me out***
Here is the answer:...
Answer:
- Solve for y
- Subtract 2 x from both sides of the equation then divide by 5 .
-y = 1 − 2 x 5
Step-by-step explanation:
Which pattern folds into the triangular prism above?
Answer:
the pattern would be W
Step-by-step explanation:
W should be the answer. Hope I helped you lots please count me brainy
The weights of five dogs are 83 pounds, 94 pounds, 89 pounds, 94 pounds, and 90 pounds. What is the mean weight of the dogs?
Answer:
90
Step-by-step explanation:
add them all up and divide by how many there are
The answer is 90.
Add all the numbers then average them out by how many numbers there are.
the Johnsons want to cover their backyard with new grass their backyard is rectangular with a length of 3x - 2 feet and a width of 3x + 1 ft however there rectangular swimming pool along with its surrounding patio has dimensions of x + 4 by x + 5 ft what is the area of the region of the yard that they want to cover with new grass
The answer is:
The area that the want to cover with new grass will be:
[tex]Area_{grass}=8x^{2} -12x-22[/tex]
Why?If we want to calculate what is the ara of the region of the backyard that they want to cover with new grass, we need to calculate the area of the backyard, calculate the area of the swimming pool and its patio, and the last step is to subtract the area of the swimming pool and its patio to the total area of the backyard.
So, to calculate the areas, we need to use the following formula:
[tex]Area=Length*Width[/tex]
Also, we need to remember how the distributive property works, since we are going to need it.
We have that:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
We are given the following information:
For the backyard we have:
[tex]Length=3x-2\\Width=3x+1[/tex]
For the swimming pool and its patio:
Since there it's not mentioned, let be the first expression the length, and the second one, the width.
[tex]Length=x+4\\Width=x+5[/tex]
Then, calculating we have:
Backyard:
[tex]Area_{backyard}=(3x-2)*(3x+1)=9x^{2}+3x-6x-2=9x^{2}-3x-2[/tex]
Swimming pool and patio:
[tex]Area_{swimmingpool}=(x+4)*(x+5)=x^{2}+5x+4x+20=x^{2}+9x+20[/tex]
Now, calculating the area that they want to cover with new grass, we have:
[tex]Area_{grass}=Area_{backyard}-Area_{swimmingPool}\\\\Area_{grass}=(9x^{2}-3x-2)-(x^{2}+9x+20)\\\\Area_{grass}=9x^{2} -x^{2} -3x-9x-2-20\\\\Area_{grass}=8x^{2} -12x-22[/tex]
Hence, we have that the area that the want to cover with new grass will be:
[tex]Area_{grass}=8x^{2} -12x-22[/tex]
Have a nice day!
What is the 25th term of this arithmetic sequence? 3, 9, 15, 21, 27, …
Answer:
147
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
here a = 3 and d = 9 - 3 = 15 - 9 = 6, hence
[tex]a_{25}[/tex] = 3 + (24 × 6) = 3 + 144 = 147
Use the graph to write the factorization of x^2+2x-8
Answer:
(x-2)(x+4)
Step-by-step explanation:
So it would be A.
Explanation: The middle number is 2 and the last number is -8.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 2
Multiply together to get -8
Can you think of the two numbers?
Try -2 and 4:
-2+4 = 2
-2*4 = -8
Fill in the blanks in
(x+_)(x+_)
with -2 and 4 to get...
(x-2)(x+4)
Answer:
(x−2)(x+4)
A. (x+4)(x-2). The factorization of the quadratic equation x²+2x-8 given by the graph is (x+4)(x-2).
From the graph shown in the image we can see the parabola's cut points, in the y-axis is -4 and the x-axis is 2, then we write the product changing the signs (x+4)(x-2) = x²+2x-8
Lonnie divides a pipe into 10 inch sections. Each section represents 1/8 of the pipe’s length. What is the original length of the pipe?
Answer:
80 inches
Step-by-step explanation:
8*10=80
Answer:
80 in.
Step-by-step explanation:
So we know that 1/8 is 10 in.
So to get 8/8 (Original length), we need to multiply 10 by 8, because 8 is the denominator.
10 in * 8 = 80 in.
Hope I beat Jarid lol
What is the area the of the figure below? A) 26 B) 27 C) 52 D) 54
Answer: B=27
Step-by-step explanation:
10.8 x 5=54/2= 27
Answer:
26in.^2 the first choice
Step-by-step explanation:
Just did the QC
Line AB contains points A (0, 1) and B (1, 5). The slope of line AB is
−4
negative 1 over 4
1 over 4
4
solution here,
slope(m)=(y2-y1)/(x2-x1)
=(5-1)/(1-0)
=4/1 =4
Answer:
The correct answer is D) 4
Step-by-step explanation:
I took the test and this was correct!
why isit posible to calculate the volume of a skewed prism or oblique cylinder with the same formula as the euation for the volume of a right prism or cylinder?
Answer:
The volume of oblique cylinders is the same volume as a right cylinder of the same radius and height. The height of cylinder must be the perpendicular height, but as long as the radius and height are the same the volume does not change, which is why the same formula can be used for both oblique and right cylinder.
For skewed and right prism, base length and height does not change, volume for both is calculated by area times height.
HElp i need help and explanations plz
Answer:
[tex] \frac{1}{2} \times 21.6 \times 5.9 = 63.72[/tex]
The area of this triangle is 63.72 square feet.
Find the perimeter or cm
Answer:
The perimeter is 22.
Step-by-step explanation:
The perimeter formula (it sometimes varies) is 2(b+h)
b being base (in this example, 6)
h being height (in this example, 5)
So now, with substitution, we are left with:
2(6+5)
Which simplifies down to:
2(11)
22
Can someone help me please
Answer:
L.A. = 60π m² ≈ 188.4 m²S.A. = 85π m² ≈ 266.9 m²Step-by-step explanation:
Lateral Area:
The formula of a Lateral Area of a cone:
[tex]L.A.=\pi rs[/tex]
r - radius
s - slant height
We have r = 5m and s = 12m. Substitute:
[tex]L.A.=\pi(5)(12)=60\pi\ m^2\\\\\pi\approx3.14\to L.A.\approx(6)(3.14)=188.4\ m^2[/tex]Surface Area:
The formula of a Surfaace Area of a cone:
[tex]S.A.=B+L.A.[/tex]
In the base we have the circle with the radius r = 5m.
The formula of an area of a circle"
[tex]A_O=\pi r^2[/tex]
Substiute:
[tex]B=\pi(5^2)=25\pi\ m^2\approx(25)(3.14)=78.5\ m^2[/tex]
[tex]S.A.=60\pi+25\pi=85\pi\ m^2\approx188.4+78.5=266.9\ m^2[/tex]
The population of a heard of cattle numbered was 5000 to begin with and was 10,000 after 10 years. If the population was growing exponentially, what was the growth rate? show all work
A) r=2
B) r=20
C)r=0.69
D)r=6.9
Answer:
[tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69
Step-by-step explanation:
To solve this we are using the standard exponential growth equation:
[tex]f(t)=A(1+r)^t[/tex]
where
[tex]f(t)[/tex] is the final population after [tex]t[/tex] years
[tex]A[/tex] is the initial population
[tex]r[/tex] is the growth rate in decimal form
[tex]t[/tex] is the time in years
We know from our problem that the initial population is 5000, the final population is 10000, and the time is 10 years, so [tex]A=5000[/tex], [tex]f(t)=10000[/tex], and [tex]t=10[/tex].
Let's replace the values and solve for [tex]r[/tex]:
[tex]f(t)=A(1+r)^t[/tex]
[tex]10000=5000(1+r)^{10}[/tex]
Divide both sides by 5000
[tex]\frac{10000}{5000} =(1+r)^{10}[/tex]
[tex]2=(1+r)^{10}[/tex]
Take root of 10 to both sides
[tex]\sqrt[10]{2} =\sqrt[10]{(1+r)^{10}}[/tex]
[tex]\sqrt[10]{2} =1+r[/tex]
Subtract 1 from both sides
[tex]\sqrt[10]{2}-1=r[/tex]
[tex]r=\sqrt[10]{2}-1[/tex]
[tex]r=1.0718-1[/tex]
[tex]r=0.0718[/tex]
We can conclude that the growth rate of our exponential equation is [tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69
Simplify ( √ 5)(^3 √ 5) the answer will be a wholenumber and a fraction
[tex]( \sqrt{5)( \sqrt[3]{5} } )[/tex]
Answer:
[tex]\sqrt{5}\cdot\sqrt[3]{5} =\sqrt[6]{5^3} \cdot\sqrt[6]{5^2} =\sqrt[6]{5^5} =5^{(5/6)}[/tex]
Step-by-step explanation:
The rules of exponents apply, even when they are fractional exponents:
[tex]a^b\cdot a^c=a^{b+c}\\\\\sqrt[b]{x^a}=x^{(a/b)}[/tex]
Use Julia’s work and finish finding the areas of the faces what is the surface area of the rectangular pyramid
Answer:
The surface area of the rectangular pyramid is [tex]SA=109.50\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to the area of the rectangular base plus the area of the four triangular faces
so
[tex]SA=(8)(5)+2[14.75]+2[\frac{1}{2}(8)(5)][/tex]
[tex]SA=40+29.50+40[/tex]
[tex]SA=109.50\ m^{2}[/tex]
Answer:
109.5
Step-by-step explanation:
Please this is urgent !
Answer:
the probability is very high 86% > 14%
Step-by-step explanation:
55+20+11= 86%/100% 100-86=14% chance there will not be any rain or lightning
hope this helps!!
Divide. Write your answer in simplest form.
8÷7/6
Answer:
4/21
Step-by-step explanation:
In this case, carry out the indicated operations from left to right:
8 1
---- * --- = 4/21
7 6