Answer:
C. P= 1000M
Step-by-step explanation:
[tex]log(\frac{M}{N} )=4[/tex]
Using the quotient rule of logs we can write:
log(M) - log(N) = 4
or
log(M) - 4 = log(N) (Equation 1)
[tex]log(\frac{P}{N} )=4[/tex]
Using the quotient rule of logs we can write:
log(P) - log(N) = 7
or
log(P) - 7 = log(N) (Equation 2)
Comparing equation 1 and 2, we can write:
log(M) - 4 = log(P) - 7
-4 + 7 = log(P) - log(M)
log(P) - log(M) = 3
[tex]log(\frac{P}{M} )=3[/tex]
Converting the log to exponential form we get:
[tex]\frac{P}{M}=10^{3}\\\\\frac{P}{M}=1000\\\\P=1000M[/tex]
Thus, option C gives the correct answer.
Final answer:
The relationship between M and P is that P is 1000 times greater than M; hence, the correct option is P = 1000M.
Explanation:
Given the two equations log(M/N) = 4 and log(P/N) = 7, we need to find the relationship between M and P.
To understand this relationship, we use the property of logarithms that equates to a multiplication by 10 for each unity increase in logarithmic value.
From the first equation, M/N = 10⁴, and from the second equation, P/N = 10⁷. Simplifying these, M = 10⁴ N and P = 10⁷ N.
To find the relationship between M and P, we can divide the equation for P by the equation for M:
P/M = (10⁷ N) / (10⁴ N) = 10³ = 1000.
Therefore, P is 1000 times M, which means P = 1000M
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!
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
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
-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.
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.
Jerry made 4 pitchers of grape juice and 6 pitchers of orange juice. Each pitcher contains 64 oz of juice. Which explanation correctly tells how to calculate the number of ounces of juice Jerry made in all? A. Step 1 Multiply 64 × 4. Step 2 Multiply 64 × 6. Step 3 Subtract the products. B. Step 1 Add 4 + 6. Step 2 Multiply that sum by 64. C. Step 1 Divide 64 ÷ 4. Step 2 Multiply 64 × 6. Step 3 Add the quotient and product. D. Step 1 Subtract 6 – 4. Step 2 Multiply that difference by 64.
Answer:
B
Step-by-step explanation:
Given
pitchers of grape juice=g=4
picthers of orange juice=o=6
Each pitcher contains 64 oz of juice
So in order to calculate, we will calculate the total number of pitchers and then multiply it by 64 to get total oz.
=(6+4)*64
=10*64
=640 oz
We can see that we added count of pitchers and then multiplied the sum by 64.
So option B is the correct answer ..
I think either A or D makes more sense
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
Equation of line in slope intercept form
Answer ASAP
Answer:
[tex]\large\boxed{y=0.470793x+2.13908}[/tex]
Step-by-step explanation:
The slope intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
From your picture we have:
[tex]m=0.470793[/tex]
and
[tex]b=2.13908[/tex]
Substitute:
[tex]y=0.470793x+2.13908[/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:
I'm having trouble figuring out how to find the right symbol for this problem √9=6 ? 3
Answer:
It's a - (minus) sign.
Step-by-step explanation:
This is because √9 is 3, and therefore 6-3=3.
Hope I helped :)
A prism is filled with 30 cubes with 1/2 unit side lengths. What is the volume of the prism in cubic units?
The correct anwser would be 56
The volume of the prism filled with 30 cubes with side lengths of 1/2 unit is 3.75 cubic units.
To calculate the volume of a cube with a side length of 1/2 unit, we use the formula V = s³, where s is the side length of the cube.
For a side length of 1/2 unit, the volume of one cube is V = (1/2)³ cubic units.
Therefore, the volume of one such cube is 1/8 cubic units. If the prism is filled with 30 such cubes, we multiply the volume of one cube by the number of cubes:
Total Volume = Number of Cubes × Volume of One Cube = 30 × 1/8 cubic units = 30/8, which simplifies to 3.75 cubic units.
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]
Which is a simplified form of the expression -2(x – 9) – x?
A. -3x + 18
B. 3x – 18
C. x – 9
D. x + 18
multiply the bracket by 2
-2x+18-x
Negative and Negative= positive
=-3x+18
Answer:A
Answer:
The answer is A
Step-by-step explanation:
Solve for x x^2-2x-24= 0
Step-by-step explanation:
I think the answer is x=-4,x=+6
The values of the x are +6 and -4. The values of the x are obtained by the factorization method.
What exactly is a polynomial?
They are mathematical formulas containing variables raised by non-negative integers, coefficient, and constants involving only addition, subtraction, multiplication, and non-negative exponentiation of variables.
The given expression is;
x²-2x-24= 0
By factorization;
x²-6x+4x-24=0
After taking common terms, we get ;
x²-6x+4x-24=0
x(x-6)+4(x-6)=0
(x+4)(x-6)=0
The value of the x is found as;
x-4=0
x=-4
x-6=0
x=+6
Hence, the values of the x are +6 and -4.
To learn more about polynomials, refer:
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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.
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
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.
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
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.
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
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
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!
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!
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**
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
Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? Explain.
Answer:
Sample Response: Gerard determined that the squares of the two smaller sides did not equal the square of the longest side. The side lengths did not create a true statement of the Pythagorean theorem.
Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.
What is the Pythagorean Theorem?The Pythagorean Theorem states that the sum of the squares of the two smaller legs of a right triangle equals the square of the longer side.Thus, if a and b are the length of the two smaller sides of a right triangle, and c is the longest side, then: a² + b² = c².Therefore, Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.
Learn more about the Pythagorean Theorem on:
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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!!
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
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.