Answers
Answer:
The option is C
Step-by-step explanation:
The solution is in the image
Use the rules of exponents and logarithms to solve the equation.
\(\bf{\dfrac{1}{16}\times4^{x}=64 }\)
Multiply both sides by 16.
\(\bf{4^{x}=1024 }\)
Take the logarithm of the two sides of the equation.
\(\bf{log(4^{x} )=log(1024) }\)
The logarithm of a number raised to a power is the power multiplied by the logarithm of the number.
\(\bf{x \ log(4)=log(1024) }\)
Divide the two sides by log(4).
\(\bf{x=\dfrac{log(1024)}{log(4)} }\)
By the base change formula \(\bf{\frac{log(a)}{log(b)}=log_{b}(a). }\)
\(\bf{x=log_{4}(1024) }\)
x = 5 ====> Answer
Option CRelated Questions
3x – 5 =-10
6. To solve the equation in the box for the
value of x, Michele started by adding 5 to both
sides. To get the correct answer, what must
Michele do next?
A divide both sides by 10
B. divide both sides by 3
C. multiply both sides by 10
D. multiply both sides by 3
Answers
After adding 5 to both sides what did Michele get? Let's see
\(3x-5 + 5 = -10 + 5\\3x= -5\)
If she wants to find the value of \(x\) then she needs to have only the variable \(x\) on the left hand side. What she must do so that \(3x\) becomes just \(x\)? What do you have to do to the number 3 so it becomes a 1? That's right, she must divide by 3!
So, after dividing both sides by 3:
\(\frac{3x}{3} = \frac{-10}{3} \\\\\boxed{x=\frac{-10}{3}}\)
Thus, the correct answer is letter B
Write an equation of the line that passes through (18, 2) and is parallel to the line 3y - x= -12.
please help!!
Answers
An SEO account manager is concerned website developers are using too many keywords per web page. The SEO account manager would like to carry out a hypothesis test and test the claim that a web page has, on average, more than 10 keywords. Why is this hypothesis test right-tailed
Answers
Answer:
The hypothesis test is right tailed because of claim made by SEO account manager that a web page on average has more than 10 keywords.
Step-by-step explanation:
The given hypothesis test is right tailed due to the claim made by SEO account manager. The tail of hypothesis test decided by looking at alternative hypothesis. The claim stated as " a web on average has more than 10 keywords" and this leads to alternative hypothesis as
Ha:μ>10.
The alternative hypothesis shows the greater than area or also known as right tailed area. Thus, given hypothesis test is right tailed.
x-4y=2 x-2y=-1 what is x and y
Answers
Answer: Um, I think that the answer to this math question about solving for x and y with the given algebraic equation form are \(x=-\frac{1}{3}\) and \(y=\frac{1}{6}.\)
Step-by-step explanation: First, here are 3 alternative form steps in order to solve for x and y with the given algebraic equation form that looks in the algebraic step-by-step equation forms like this:
Step 1. {y = x/4 + 1/4, y = x + 1/2}.
Step 2. {x + 1 = 4y, 2x + 1 = 2y}.
Step 3. {x - 4y = -1, 2(x - y) = -1}.
Therefore, your real solution answer to this math question about solving for x and y with the given algebraic equation form are \(x=-\frac{1}{3}\) and \(y=\frac{1}{6}.\)
Finally, here is an implicit plot that looks in the graphing form image like this, but I hope that my full given answer with my full given step-by-step explanation is very helpful to your own math question about solving for x and y with the given algebraic equation form, please mark me as Brainliest, take care, always be safe, and have a great rest of the holiday winter break, Merry Christmas and a happy new year! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
Mr. Kelsey just opened a T‑shirt shop and is determining what to charge for bundles of shirts. Which table of prices represents a proportional relationship?
Answers
Answer:i may not be right but i think its A
Answer:
B is correct
Step-by-step explanation:
1 ft. 3 in. Is what part of 1 yd? I need this please I don’t get how to solve it
Answers
if the letter l,o,g,ic are randomnly arranged to form word logic what is the probability that result will be woord logic
Answers
The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))
To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.
The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.
The total number of possible arrangements is given by the factorial of the total number of letters:
Total arrangements = 10!
However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:
Total arrangements = 10! / (2!)
To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.
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1. The table represents a quadratic function. Write an equation of the function in standard form. X f(x) -4 -3 -2 0 0 1 2 0
Answers
An equation of the function in standard form is equal to -x²/4 + 1 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-3 = a(-4)² + b(-4) + c ⇒ -3 = 16a - 4b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
1 = a(0)² + b(0) + c ⇒ 1 = c .......equation 3.
Substituting the value of c into eqn. 1 and eqn. 2, we have:
-4 = 16a - 4b .......equation 4.
-1 = 4a - 2b .......equation 5.
Multiplying eqn. 5 by 2 and solving simultaneously, we have:
-4 = 16a - 4b
-2 = 8a - 4b
-2 = 8a
a = -2/8
a = -1/4
For the value of b, we have:
-1 = 4a - 2b
-1 = 4(-1/4) - 2b
-1 = -1 - 2b
2b = 0
b = 0
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-1/4x² + (0)x + 1 = 0
-x²/4 + 1 = 0
Check:
When x = 2, we have:
-x²/4 + 1 = 0
-2²/4 + 1 = 0
-4/4 + 1 = 0
-1 + 1 = 0
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Determine how many integer solutions there are to
x₁ + x₂ + x3 + x₁ = 20, if
0≤x₁ < 3, 0≤ x₂ < 4, 0≤x3 <5, 0≤x4 < 6
Answers
Based on the information given, there are a total of 118 solutions.
How many possible solutions are there?This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:
x1 + x2 + x3 + y4 = 20
Subject to the following conditions:
0 ≤ x1 < 3
0 ≤ x2 < 4
0 ≤ x3 < 5
0 ≤ y4 < 6
We can solve this problem using the technique of generating functions. The generating function for each variable is:
(1 + x + x^2) for x1
(1 + x + x^2 + x^3) for x2
(1 + x + x^2 + x^3 + x^4) for x3
(1 + x + x^2 + x^3 + x^4 + x^5) for y4
The generating function for the equation is the product of the generating functions for each variable:
(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)
We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118
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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.
Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:
**|**||
then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.
In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).
Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:
C(20+4-1, 4-1) = C(23, 3) = 1771
However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.
Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:
A = A₀ ∩ A₁ ∩ A₂ ∩ A₃
where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.
To find the cardinality of A₀, we use the formula above and obtain:
C(20+4-1, 4-1) = 1771
To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:
C(20-4+3-1, 3-1) = C(18, 2) = 153
Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:
|A| = |A₀| - |A
Step-by-step explanation:
The quilt has 5 parallelograms. Each parallelogram has a base of 10 inches and a height of
7 inches. What area of the quilt is covered by the parallelograms?
Answers
Answer:
350 in. squared
Step-by-step explanation:
15)
136⁰
2
S
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R
Find the measure of the arc or angle indicated
Answers
Answer:
224
Step-by-step explanation:
360.-136.
State the domain and range of the following function.
Answers
Answer:
Step-by-step explanation:
ur STUP1d
In ΔQRS, m∠R = 57°, q = 9, and s = 5. Find the area of ΔQRS.
Answers
The area of ΔQRS is 26.10 square units.
What is triangle?
A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.
To find the area of \($\triangle QRS$\), we can use the formula:
\($Area = \frac{1}{2} \times base \times height$\)
where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.
First, we need to find the length of side \($QR$\). We can use the Law of Cosines:
\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)
where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:
\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)
\($QR \approx 8.02$\)
Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:
\($\sin(R) = \frac{opposite}{hypotenuse}$\)
\($\sin(57^\circ) = \frac{height}{8.02}$\)
\($height \approx 6.51$\)
Now we can find the area of the triangle:
\($Area = \frac{1}{2} \times QR \times height$\)
\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)
\($Area \approx 26.10$\) square units
Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.
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Christie makes changes to her budget at the end of every month. What is her reason for doing this in terms of smart financial planning?
A.
She keeps changing her mind about her goals.
B.
She is reviewing her goals and aligning the budget to work toward them.
C.
Her needs keep changing, so she changes her monthly budget.
D.
She realizes that her budget is tightly aligned to her goals.
Answers
The most appropriate reason for Christie making changes to her budget at the end of every month in terms of smart financial planning is B. She is reviewing her goals and aligning the budget to work toward them.Option B is correct.
Smart financial planning involves regularly evaluating and adjusting one's budget to ensure that it reflects their financial goals and current circumstances. By reviewing her goals, Christie can assess if her budget is still aligned with those goals and make any necessary changes to stay on track.
Life circumstances, such as changes in income, expenses, or financial priorities, may warrant adjustments to the budget. Christie recognizes that her needs may change over time, and by modifying her monthly budget, she can ensure that her financial resources are allocated appropriately to meet her evolving goals.
Regularly revisiting and modifying the budget allows Christie to adapt her financial plans, optimize her spending, and make informed decisions to achieve her financial objectives. Option B is correct.
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i need help with this question please
Answers
Answer: it C
Step-by-step explanation: if it not incorrect sorry for the wrong answer
Unions, intersections, and complements involving 2 sets
Sets B and C are subsets of the universal set U.
These sets are defined as follows.
U={f, k, m, s, x, y, z)
B={k, s, y}'
C={s,z}
(a) B'UC' = 1
(b) B'nc =
Answers
Intersection of B'∩C = {k, y}
To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.
1. Complement of set B (B'):
The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.
2. Intersection between B' and C:
Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.
The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.
So, the answer to (b) is B'∩C = {k, y}.
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Given a data set of all positive values, if the smallest value of a data set is divided by two, which of the following is not true?
a) The standard deviation increases.
b) The interquartile range increases.
c) The range increases.
d) The mean decreases.
Answers
What is the simplest
Answers
Answer:
(c) x³·∛x
Step-by-step explanation:
You want the simplified form of ∛(x¹⁰).
Cube rootsThe first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.
\(\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}\)
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Last year, Gina's sweet potato farm produced 337 tons of sweet potatoes. This year, the sweet potato production increased by 40%. How many tons of sweet potatoes did Gina's farm produce this year? 427 tons 425 tons 447 tons 445 tons
Answers
So, Gina's farm produced approximately 471.8 tons of sweet potatoes this year. Rounded to the nearest whole number, this is 472 tons.
What you mean by increasing?When we talk about an increase, we are referring to a change in quantity or value that is greater than the original amount. In other words, an increase means that something has gotten bigger, larger, or more than it was before.
Given by the question.
To find out how much sweet potatoes Gina's farm produced this year, we need to add 40% of last year's production to the amount produced last year:
40% of 337 tons = 0.4 x 337 = 134.8 tons
Adding this to last year's production gives:
337 + 134.8 = 471.8 tons
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The Oriental Pearl Tower in Shanghai, China, is a 468-meter high tower with 11 spheres along the tower. Two spheres are larger than the rest and house meeting areas, an observation deck, and a revolving restaurant. The lower of the two larger spheres has a radius of 25 meters, and the higher sphere has a radius of 22.5 meters. What is the approximate total volume of the two largest spheres on the Oriental Pearl Tower?
Answers
The approximate total volume of the two largest spheres on the Oriental Pearl Tower 113105.45 m³.
How to find the volume of a sphereThe volume of the sphere is calculated as follows:
volume = 4 / 3 πr³
where
r = radiusThe lower two larger spheres in the tower has a radius of 25 meters and 22.5 meters. Therefore, the total volume of the two largest sphere is as follows:
volume of lower sphere = 4 / 3 × 3.14 × 25³
volume of lower sphere = 196250 / 3
volume of lower sphere = 65416.6666667
volume of lower sphere = 65416.7 m³
volume of higher sphere = 4 / 3 × 3.14 × 22.5³
volume of higher sphere = 143066.25 / 3
volume of higher sphere = 47688.75
volume of higher sphere = 47688.8 m³
The approximate total volume = 65416.7 + 47688.8 = 113105.45 m³
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brainy heart rate 190 per minute her heart rate is 70% of her MHR
what is target heart rate
70
120
133
190
217
Answers
Answer:
120
Step-by-step explanation:
trough dependent sarcasm
Help anyone and can anyone explain this too!
Answers
Answer:
X = 9
Step-by-step explanation:
Vertical angles equal to each other, the example shows vertical angles.
6x + 2 = 54
-2 -2
6x/6 = 54/6
X = 9
Hope this helps you have a nice day!
The width of a rectangle is 4 less than half the lenght. If L represents the length, which equation could be used to find the width, w?
Answers
Answer:
Step-by-step explanation:
Find the midpoint of a segment. It is geometry please help.
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
Answers
The coordinate of the point after transformation is: (3, -4)
What is the coordinate after moving of point?The coordinate initially is given as (0, -4).
Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:
(0 - 1, -4)
= (-1, -4)
Moving by 4 units to the right means an addition of 4 units to x coordinate to get:
(-1 + 4, -4)
= (3, -4)
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How do you solve 8^2
Answers
To solve 8^2 , we have to multiply 8 with itself , this means = 8 × 8 = 64 . Thus, our answer = 8²= 64.
This also known as square of a number as we multiply it with itself .
Find -1/5 + (-3/5) in simplest form
Answers
Answer: -0.8 or -4/5
Step-by-step explanation:
1/5 + 3/5 = 4/5 and u put the negatives so its -4/5. HOPE THIS HELPS :3 !!!!
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Answers
Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.
To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.
The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.
Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.
To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:
£72 / 5 = £14.40
Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.
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Solve for x & show steps
2000 = 400√x
Answers
x=25
Step-by-step explanation:
2000=400√x
Step 1: Flip the equation.
400√x=2000
Step 2: Divide both sides by 400.
400√x/400=2000/400
√x=5
Step 3: Solve Square Root.
√x=5
x=52(Square both sides)
x=25
Check answers. (Plug them in to make sure they work.)
x=25
The effect of wearing different types of running shoes on the time it takes to complete a race is being studied in experiment. which of these is most likely to be an extraneous factor that could also affect the time it takes to complete the race?
Answers
Answer:
A. Weather conditions
Step-by-step explanation:
find the product in lowest terms 24/18x2/17x34/3
Answers
Answer:
Step-by-step explanation:
To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:
(24/18) * (2/17) * (34/3)
First, we can simplify the fractions by reducing any common factors in the numerators and denominators:
24/18 = (212)/(29) = 12/9 = 4/3
2/17 = 2/17
34/3 = (2*17)/3 = 34/3
Now we can multiply the simplified fractions:
(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153
The product of the given fractions in lowest terms is 272/153.