To write log8 3 as a logarithm of base 5, we can use the change of base formula: loga b = logc b / logc a. Applying this formula, we have log5 3 = log8 3 / log8 5. Therefore, the correct option is (log8)5/(log3)5.
Explanation:The expression log83 represents the logarithm of 3 with base 8. To write it as a logarithm with base 5, we can use the change of base formula:
logab = logcb / logca
Applying this formula, we have:
log53 = log83 / log85
Therefore, the correct option is (log8)5/(log3)5.
Maya has 5 over 6 cup of ice cream. how many 1 over 4-cup servings are in 5 over 6 cup of ice cream?
there are [tex]\( \frac{10}{3} \) or \( 3 \frac{1}{3} \) servings of \( \frac{1}{4} \)-cup in \( \frac{5}{6} \)[/tex] cup of ice cream.
To find out how many [tex]\( \frac{1}{4} \)-cup servings are in \( \frac{5}{6} \)[/tex] cup of ice cream, we need to divide [tex]\( \frac{5}{6} \) by \( \frac{1}{4} \)[/tex].
We can do this by converting [tex]\( \frac{5}{6} \)[/tex] to have the same denominator as [tex]\( \frac{1}{4} \)[/tex], which is 6, and then dividing:
[tex]\[ \frac{5}{6} \div \frac{1}{4} \][/tex]
To make the denominators the same, we multiply both the numerator and denominator of [tex]\( \frac{5}{6} \) by \( 4 \):[/tex]
[tex]\[ \frac{5 \times 4}{6 \times 4} \div \frac{1}{4} \][/tex]
[tex]\[ = \frac{20}{24} \div \frac{1}{4} \][/tex]
Now, we can divide [tex]\( \frac{20}{24} \) by \( \frac{1}{4} \):[/tex]
[tex]\[ \frac{20}{24} \div \frac{1}{4} \][/tex]
[tex]\[ = \frac{20}{24} \times \frac{4}{1} \][/tex]
[tex]\[ = \frac{20 \times 4}{24 \times 1} \][/tex]
[tex]\[ = \frac{80}{24} \][/tex]
Now, we simplify the fraction:
[tex]\[ \frac{80}{24} = \frac{10 \times 8}{12 \times 2} \][/tex]
[tex]\[ = \frac{10}{3} \][/tex]
Therefore, there are [tex]\( \frac{10}{3} \) or \( 3 \frac{1}{3} \) servings of \( \frac{1}{4} \)-cup in \( \frac{5}{6} \)[/tex] cup of ice cream.
Write two equivalent fractions for each. 1/2 and 4/5
find the nonpermissible replacement for the variable n in this expression (n-8)/(n-8)
...?
Monica paid sales tax of 1.50$ when she bought a new bike helmet.if the sales tax rate was 5% how much did the store charge for the helmet before tax
Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
The correct answer is D. on edg
Shane and his family go to the movie theatre and buys 6 tickets for $12 each. then they spend a total of $31 for popcorn and drinks. how much did shane and his family spend for tickets, popcorn, and drinks at the movie theatre?
Shane and his family spent a total of $103 at the movie theatre, which includes the cost of 6 tickets at $12 each and $31 on popcorn and drinks.
Explanation:Shane and his family bought 6 tickets for $12 each, thus the total cost of the tickets is 6 * $12 which equals $72. Afterwards, they spent an additional $31 on popcorn and drinks. To find out how much they spent altogether at the movie theatre, we have to add the cost of the tickets and the cost of the popcorn and drinks. Therefore, $72 (for the tickets) + $31 (for the snacks) = $103. So, Shane and his family spent a total of $103 at the movie theatre.
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Why is it a good idea to check to see if your answer is reasonable?
Sometimes we can miss steps or incorrectly do a step. When we solve the equation we might think we have the right answer. If you double check your answer and input your answer into the equation, you can see if it is truly correct. Doing this makes sure that you won't get the question wrong
Fill in the blanks: When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the _____ of the radical, and the numerator becomes the _____ of the ______.
When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the index of the radical, and the numerator becomes the exponent of the radicand.
What is a expression? What is a mathematical equation? What are exponents and radicals?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. An exponent is just a convenient way of writing repeated multiplications of the same number. Radicals involve the use of the radical sign. These are also called surds.We have to fill the given blanks as given in question.
The complete statement is -
When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the index of the radical, and the numerator becomes the exponent of the radicand.
Therefore, the complete statement is -
When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the index of the radical, and the numerator becomes the exponent of the radicand.
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Which ratio is equal to 5/6 and
Which ratio is not equal to 4/9? ...?
What is the completely factored form of 3x^5 – 7x^4 + 6x^2 – 14x?
A. (x^4+2x)(3x-7)
B. x^4(3x-7)(2x-1)
C. x(x^3+2)(3x-7)
D. x(3x^4-7x^3+6x-14)
answer:
C. x(x^3+2)(3x-7)
hope this helps! :o)
Breann solved the system of equations below. What mistake did she make in her work? (5 points)
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 20
x = 4
2(4) + y = 5
y = −3
She should have substituted 5 + 2x
She combined like terms incorrectly, it should have been 4x instead of 5x
She subtracted 10 from both sides instead of adding 10 to both sides
She made no mistake
Breann correctly solved the system of equations, combining like terms accurately to find x = 4 and y = -3.
Explanation:The mistake Breann made in her calculation was combining like terms incorrectly. When she substituted y with 5 - 2x into the second equation, she arrived at x - 10 + 4x = 10. The correct combination of like terms should be 5x, not 4x, leading to the correct step 5x - 10 = 10. All other steps in her solution are correctly executed. She correctly found the value of x to be 4, and using the first equation, she correctly determined the value of y to be -3.
The label on the car's antifreeze container claims to protect the car between −30°C and 130°C. To convert Celsius temperature to Fahrenheit temperature, the formula is C = (F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.
−30 > (F − 32) > 130; −22 > F > 266
−30 < (F − 32) < 130; −22 < F < 266
−30 < (F − 32); −22 < F
(F − 32) < 130; F < 266
The correct answer is B. I took the same test and the answer is B. :) Hope this helps!
in order for RECT to be a rectangle, what must the value of x be?
Answer:
x = 21
Step-by-step explanation:
If RECT is a rectangle, each of its interior angles are right angles, 90°. Since ∠RTC is split into two angles, the sum of the two angles must be 90°. (Angles that add to 90° are called complementary angles).
∠RTC = ∠RTE + ∠ETC Formula for complementary angles
90 = 2x + 6 + 42 Substitute the angles
90 = 2x + 48 Combined like terms to simplify
Now isolate "x" to solve
90 - 48 = 2x + 48 - 48 Subtract 48 from both sides
42 = 2x
42/2 = 2x/2 Divide both sides by 2
x = 21
Therefore x is 21.
Multiply. write in simplest form fraction 6 1 1\2
Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.19 percent a year and that the 1988 population was 6.9 million, write an expression for the population as a function of time in years. (Let t=0 in 1988.)
P=?
hint: logistic function
Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.19 percent a year and that the 1988 population was 6.9 million, write an expression for the population as a function of time in years. (Let t=0 in 1988.)
P=?
Answer:
[tex]P(t) = 6900000 e^{0.0019t}[/tex]
Step-by-step explanation:
Equation for an exponential growth:
[tex]P(t) = P_{0} e^{kt}[/tex].............(1)
Where [tex]P_{0}[/tex] = The initial population of Switzerland at time t = 0
At t = 0 in 1988, the population was [tex]P_{0} = 6.9 million[/tex]
k = 0.19% = 0.19/100 = 0.0019
The population as a function of time becomes:
[tex]P(t) = 6900000 e^{0.0019t}[/tex]
Final answer:
The expression for Switzerland's population growing exponentially at a 0.19 percent yearly rate from a 1988 population of 6.9 million is calculated using the exponential growth formula, resulting in P = 6.9e^0.0019t.
Explanation:
Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.19 percent a year and that the 1988 population was 6.9 million, the expression for the population as a function of time in years is derived using the equation for continuous exponential growth. Let t=0 in 1988, then the population at any year t can be given by the formula P = P0ert, where P0 is the initial population, r is the rate of growth, and e is the base of the natural logarithms. Here, P0 = 6.9 million and r = 0.0019 (since 0.19% is 0.19/100 = 0.0019). Therefore, the expression for the population as a function of time in years from 1988 is P = 6.9e0.0019t.
Your friend has $80 when he goes to the fair. He spends $4 to enter the fair and $12 on food. Rides at the fair cost $1.25 per ride. Which function can be used to determine how much money he has left over after x rides?
A) f(x) = 1.25x + 64
B) f(x) = -16x + $80
C) f(x) = -1.25x + 64
D) f(x) = -1.25x - 64
Instructions:Select the correct answer from each drop-down menu.
Angle θ lies in the second quadrant, and sin θ = 35.
cos θ = -4/5 -3/5 3/5 4/5
tan θ = -4/3 -3/4 3/4 4/3
In many cases, ________ integration is more profitable than ________ integration.
Final answer:
Vertical integration may be more profitable by allowing firms to control more of the supply chain, reducing costs, and improving efficiency. It can help protect against competitive threats such as adverse selection and free riders. However, the decision depends on context, including budgetary constraints and the need to protect proprietary information.
Explanation:
In many cases, vertical integration is more profitable than horizontal integration. Vertical integration occurs when a company expands its operations into an earlier or later stage in the value chain. This approach can be advantageous because it allows a firm to control more aspects of its supply chain, which can reduce costs and improve efficiency. For example, upstream integration happens when a business expands into an earlier stage, such as a car manufacturer beginning to produce its own steel. Conversely, downstream integration occurs when the expansion is to a later stage, like a manufacturer opening retail outlets.
Decision-making in the context of integration strategies can be influenced by various factors. In situations where protecting against problems of adverse selection and free riders is difficult, vertical integration might be preferred. The concept of double marginalization, where a single vertically integrated firm can achieve higher profits than two separate firms operating at different stages of the value chain, is also a key consideration.
Nevertheless, the decision to integrate vertically or pursue other strategies depends on the specific context and the internal and external factors affecting the business. For instance, if a company holds certain production or planning secrets, vertical integration might help in safeguarding this proprietary information. Conversely, if budget constraints are a significant concern, a less costly option might be adopted even if it's not as effective as vertical integration.
A driving license number has 6 digits (between 1 to 9). The first two digits are 12 in that order, that third digit third digit is bigger than 6, the fourth one can be equally divided divided by 3 and the fifth digit is 3 times bigger than sixth one. How many license numbers can be made using this arrangement?
27, 36, 72, 112 ...?
James is participating in a 5-mile walk to raise money for a charity. he has received $200 in fixed pledges and raises $20 extra for every mile he walks. use a point-slope equation to find the amount he will raise ifhe completes the walk.
Answer:
The amount James will collect if he completes the walk is $ 300
Step-by-step explanation:
The line can be understood as an infinite set of points aligned in a single direction. A line can be expressed by an equation that follows the model y = m * x + b, where "x" e "y" are the variables in a plane. In this expression m is called the slope of the line and is related to the inclination of the line, and b is the independent term and is the value of the point at which the line cuts to the vertical axis (y axis) in the plane.
In general, the slope represents the variation of y with respect to the variation of x. That is, if the value of "x" varies, the value of "y" will also vary. On the other hand, the value of "b", being the interserction with the y-axis, means that the value of "x" must be zero. Then it represents the initial condition of the problem. Then, in this case, James has initially received $ 200 in fixed commitments, 200 being the value of "b". James raises an additional $ 20 for every mile he walks, so the value of the "m" slope is 20 and "x" represents every mile James walks.
Finally, the equation of the line represented is:
y=20*x+200
One type of linear equation is the point-slope form, which provides the slope of a line and the coordinates of a point on it. The point-slope form of a linear equation is written as
y-y1 = m (x-x1)
where m is the slope and (x1, y1) are the coordinates of the point.
In this particular case, it was mentioned that the value of the slope is 20. The values of (x1, y1) must be known. In this case, James initially received $ 200 in fixed commitments, meaning that the value of x1 = 0 and the value of y1 = 200. Replacing these values in the desired equation you get:
y-200=20*(x-0)
y-200=20*x
To find the amount that will be collected if you complete the walk, you must replace the value of x (which represents each mile walked) by 5, the distance to travel on the walk:
y-200=20*5
y-200=100
y=100+200
y=300
The amount James will collect if he completes the walk is $ 300
Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x 20.
A. A number line with an open circle on 3, a closed circle on 5, and shading in between.
B. A number line with an open circle on 3, shading to the left and a closed circle on 5, shading to the right
C. A number line with an closed circle on 3, shading to the left, and a open circle on 5, and shading to the right
D. A number line with a closed circle on 3, an open circle on 5, with shading in between.
we have in this problem
[tex] 3x+1 > 10 [/tex] ------> inequality [tex] 1 [/tex]
[tex] 4x \leq 20 [/tex] ------> inequality [tex] 2 [/tex]
Solve the inequality [tex] 1 [/tex]
[tex] 3x+1 > 10\\ 3x > 10-1\\ 3x > 9\\ x > 3 [/tex]
the solution is the interval------> (3,∞)
Solve the inequality [tex] 2 [/tex]
[tex] 4x \leq 20\\\\ x \leq \frac{20}{4} \\\\ x \leq 5 [/tex]
the solution is the interval------> (-∞,5]
Find the solution for the system
(3,∞) ∩ (-∞,5]--------> (3,5]
therefore
the answer is the option
A. A number line with an open circle on 3, a closed circle on 5, and shading in between.
Simplify completely: 3x+18 / 18
1) x
2) 3x
3) x+6 / 6
4) x+18 / 6 ...?
Answer: 3.) x+6/6
Proof of validity is shown below.
Henry is playing with a standard deck of cards what is the probability that the next card he flips over is a jack or red?
Write 3.71 as a percentage.
Natasha has a gross income of $66,429. She can make adjustments of $14,490 for business losses, $3,584 for business expenses, and $4,813 for constitutions to her retirement plan. What's Natasha's adjusted gross income?
A. $109,971
B. $22,887
C. $72,522
D. $43.542
Answer: D. $43,542
Step-by-step explanation:
The adjusted gross income of any person is person's gross income minus the certain deductions.
Given : Natasha has a gross income of $66,429.
She can make adjustments of $14,490 for business losses, $3,584 for business expenses, and $4,813 for constitutions to her retirement plan.
Total deductions : [tex]\$14,490 +\$3,584 +\$4,813=\$22,887[/tex]
Now, Natasha's adjusted gross income will be :-
[tex]\text{Gross income - Total deductions}[/tex]
i.e. [tex]\$66,429-\$22,887=\$43,542[/tex]
Hence, Natasha's adjusted gross income = $43,542
In one week, a family spent $132.19 for groceries. they spent $150.06 the next week. if c represents the increase in their grocery bill from one week to the next, what is c?
a. $17.87
b. $27.87
c. $28.97
d. $282.25
Describe the key features of the parabola y2 = 8x.
Answer: The value of p is 2. The parabola opens to the right. The focus is at (2,0). The equation of the directrix is x=-2.
Step-by-step explanation:
Divide. Express your answer in lowest terms. You MUST show your work to receive credit for this problem.
-15/16 divided by (-3/4)
Find the percent of tip:
Cost of meal $18.50, Tip $2.59
13%
14%
15%
16%
To find the percent of the tip on a meal, divide the tip by the total cost of the meal and multiply the result by 100. In this case, the tip is 14% of the cost of the meal.
Explanation:To find the percentage of the tip given on a meal, we use the formula for percent, which is part divided by whole multiplied by 100. In this case, the 'part' is the tip, which is $2.59, and the 'whole' is the cost of the meal, which is $18.50.
Step 1: Divide the tip by the cost of the meal, i.e., 2.59 / 18.50. This equals approximately 0.14.
Step 2: Multiply this result by 100 to convert it to a percentage. 0.14 * 100 equals 14.
So, the percentage of the tip given on the meal is 14%.
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Use the given endpoint R and midpoint M of line RS to find the coordinates of the other endpoins.
R(6,0), M(0,2) ...?