Answer:
j:19 days
s:23 days
23-19=4
4 days
Step-by-step explanation:
Given that the measure of ?x is 30°, and the measure of ?y is 35 °, find the measure of ?z.
To find the measure of angle z, subtract the measures of angles x and y from 180°. Therefore, angle z = 180° - 30° - 35° = 115°.
Explanation:The subject of the question is geometry, specifically dealing with the measures of angles. Without more context, it's difficult to provide an exact answer. However, if angles x, y, and z form a triangle, then the measure of angle z can be found using the property that the sum of all angles in a triangle is 180°.
To find the measure of angle z, you need to recall that the sum of the angles in a triangle is always 180°. So, you can start by finding the measure of angle z by subtracting the measures of angles x and y from 180°.
Therefore, angle z = 180° - 30° - 35° = 115°.
Learn more about Measuring Angles here:https://brainly.com/question/17413368
#SPJ2
The school fun fair made $ 1,768 on games and $978 on food sales. How much money did the fun fair make on games and food sales
If the heights of 4 family members is 153, 150, 151 and 152, find the mean height of the family.
Answer: 151.1
Step-by-step explanation:
First, you would add all the heights together (153+150+151+152=606)
Then you would divide 606 by the number of numbers in the data set in this case the number of family members which is (606 divided by 4= 151.1)
Answer:
151.5
Step-by-step explanation:
First of all, what is the mean in a set of numbers?
The mean is the average of all the numbers in the set. We can find this by finding the total value of all the terms and then dividing it by the number of terms. Let's just do a short example so we can make sure you understand.Let's look at this set of numbers:5, 3, 7, 4.To find the average of these numbers, we'll add all of the numbers and divide it by 4, the number of actual terms, in the set.
(5 + 3 + 7 + 4) / 4 = 19/4 which is also 4.75.Back to the actual problem.(153 + 150 + 151 + 152) / 4 = 151.5
let g(x)=3x+2 and f(x)= x-2/3
find the value
1.) f(g(0))
2.) g(f(2))
3.) g(g((0))
To find the values of f(g(0)), g(f(2)), and g(g(0)), substitute the given values into the functions step-by-step.
Explanation:1.) To find the value of f(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function f(x): f(2) = rac{2-2}{3} = 0.
2.) To find the value of g(f(2)), we first substitute 2 into the function f(x): f(2) = rac{2-2}{3} = 0. Then, substitute the value obtained into the function g(x): g(0) = 3(0) + 2 = 2.
3.) To find the value of g(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function g(x) again: g(2) = 3(2) + 2 = 8.
Learn more about Function Composition here:https://brainly.com/question/30143914
#SPJ12
To find the value of f(g(0)), substitute 0 into g(x) to get g(0) = 2 and then substitute this value into f(x) to get f(g(0)) = 4/3. To find the value of g(f(2)), substitute 2 into f(x) to get f(2) = 4/3 and then substitute this value into g(x) to get g(f(2)) = 8. To find the value of g(g(0)), calculate g(0) = 2 and then substitute this value into g(x) to get g(g(0)) = 8.
Explanation:To find the value of f(g(0)), we need to substitute the value of 0 into the function g(x) to get g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function f(x) to get f(2) = 2 - 2/3 = 4/3.
To find the value of g(f(2)), we need to substitute the value of 2 into the function f(x) to get f(2) = 2 - 2/3 = 4/3. Then, we substitute this value into the function g(x) to get g(4/3) = 3(4/3) + 2 = 6 + 2 = 8.
To find the value of g(g(0)), we need to calculate g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function g(x) again to get g(2) = 3(2) + 2 = 8.
Learn more about Composite Functions here:https://brainly.com/question/30143914
#SPJ12
Two small pizzas with diameter 10 cost $15, while a large pizza with diameter of 16 cost $17 which pizza is less expensive per square inch
Answer:
The larger pizza is less expensive per square inch
Step-by-step explanation:
we know that
The area of a circle (pizza) is equal to
[tex]A=\pi r^{2}[/tex]
step 1
Find the area of the smaller pizza
we have
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=(3.14)(5)^{2}=78.5\ in^{2}[/tex]
Find the price per square unit
Remember that
The price of one smaller pizza is [tex]\$15/2=\$7.5[/tex]
so
[tex]\frac{7.5}{78.5}\frac{\$}{in^{2}}=0.10\frac{\$}{in^{2}}[/tex]
step 2
Find the area of the larger pizza
we have
[tex]r=16/2=8\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=(3.14)(8)^{2}=200.96\ in^{2}[/tex]
Find the price per square unit
so
[tex]\frac{17}{200.96}\frac{\$}{in^{2}}=0.08\frac{\$}{in^{2}}[/tex]
Therefore
The larger pizza is less expensive per square inch
The length of a rectangle is three times it's width. If the perimeter of the rectangle is 64, find its length and width
set up an equation for the perimeter
l = length w = width
2l + 2w = 64
set up another equation as you know the length is 3 times the width
w = 3l
subsitute w = 3l into the 2l + 2w = 64
2l + 2(3l) = 64
solve for l
2l + 6l = 64
8l = 64
length = 8
subsitute into w = 3l
w = 3(8)
width = 24
Which statement is true? A. A triangle can be congruent to a square. B. A rectangle can be congruent to a square. C. All circles are congruent. D. None of the above is true.
➷ Congruent means it is the same shape and size. Therefore, A is incorrect as a triangle and a square aren't the same shape. The same applies to B. C is also incorrect as not all circles are the same size.
In short, the correct answer is option D. None of the above is true.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
The answer is B
Step-by-step explanation:
Congruent means In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Meaning a square and an rectangle are congruent because they both have four sides
Plus: I just took the test and got it right
Find the following measure for this figure.
Lateral area =
55 square units
5√(47) square units
5√(146) square units
Answer: last option (5π√146 units²)
Step-by-step explanation:
To solve the exercise you must apply the formula for calculate the lateral area of a cone, which is shown below:
[tex]LA=r*L*\pi[/tex]
where r is the radius but L is the slant height.
As you can see in the figure attached:
[tex]r=5[/tex]
But you need to find the slant height with the Pythagorean Theorem (L would be the hypotenuse):
[tex]L=\sqrt{11^2+5^2}=\sqrt{146}[/tex]
Substitute into the formula, then:
[tex]LA=(5)(\sqrt{146})\pi=5\pi\ \sqrt{146[/tex]units²
Answer:
The correct answer is 5√146π square units
Step-by-step explanation:
From the figure we can see a cone
Points to remember
Lateral surface area of cone = πrl
r - Radius of cone
l - Slant height of cone
To find the slant height
From figure we get,
r = 5 units and height = 11 units
Slant height² = radius² + height² = 5² + 11² = 25 + 121 = 146
Slant height = √146 units
To find the lateral area
lateral area = πrl = π * 5 * √146 = 5√146π square units
The correct answer is 5√146π square units
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 5% of its customers, how long should it make the guaranteed time limit?
Answer:
a) 11.51%; b) 13 minutes
Step-by-step explanation:
We will use a z score to answer these questions. The formula for a z score is
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For part a, X is 20, the mean is 17 and the standard deviation is 2.5:
z = (20-17)/2.5 = 3/2.5 = 1.2
Using a z table, we see the area to the left of, or less than, this value is 0.8849; this means the area to the right of, or greater than, is 1-0.8849 = 0.1151. This means 11.51% of people have a time greater than 20 minutes and get half off.
For part b, we start out in the z table finding values as close to 5%, or 0.05, as possible. There are two possibilities, 0.0505 (z=-1.64) and 0.0495 (z=-1.65). Since they are equally distant from the desired value, we will use -1.645 for z. Our values for the mean and standard deviation are the same:
-1.645 = (X-17)/2.5
Multiply both sides by 2.5:
2.5(-1.645) = ((X-17)/2.5)(2.5)
-4.1125 = X-17
Add 17 to each side:
-4.1125+17 = X-17+17
12.8875 = X
This means the garage should make the guaranteed time no more than 13 minutes.
Which system of linear inequalities is graphed?
Answer:
Should be the first one again
The dotted line is a vertical line at x -2, so we know the first equation is X<-2
The solid line means the equation has to be less than or equal to and since it crosses the dotted line at -2
the second equation would be y <=-x-2
The first choice is correct.
Question for Math.
What is 3x-1?
the answer is -3 because i searched it and that’s what came up
The answer is -3 hope this helps
Tell whether this set of numbers is a Pythagorean Triple. (6, 9, 12) Yes or no?
No it’s not a Pythagorean triple
Determine if the function f is an exponential function. If so, identify the base. If not, why not? F(x)= x^ -3
Answer:
Not an exponential function. The exponent is a constant.
Step-by-step explanation:
An exponential function has the variable in the exponent. This function raises the variable to a fixed power, so it is not an exponential function.
A chef used 1/9 of a bag of potatoes for a meal. If the potatoes fed 5 people. What fraction of the bag did each person get
1/9 has to be divided by 5 if it is shared by others.
1/9 divided by 5 is 1/45 and each person would have 1/45
Answer is 1/45
A box of 6 golf balls cost 7.32. At the rate,how much will a box of 15 golf balls cost
Answer:
$18.30
Step-by-step explanation:
First, you can figure out the cost per golf ball by dividing the price by the number of golf balls. If 6 balls = 7.32, then 1 ball = 7.32/6, or 1.22. Now you can multiply this by the number of balls in the box to find out the price: 1.22 * 15 = 18.30.
Another way to solve this is to set up a ratio of balls / price:
(x is the unknown price)
[tex]\frac{6}{7.32} =\frac{15}{x}[/tex]
Now, cross-multiplying, you find that 6x = 7.32 * 15, or 6x = 109.8. Dividing both sides by 6, you get x=18.30.
Dylan work for 4 hours and is paid 17.50 per hour he must pay 15% in income taxes what amount does he earn after taxes
Dylan earns $17.50 per hour for 4 hours, yielding a total income of $70. After deducting 15% of his total earnings ($10.50) for income taxes, Dylan's earnings reduce to $59.50.
Explanation:To answer this question, we first need to calculate Dylan's total earnings before taxes. He earned $17.50 per hour for 4 hours, so his total earnings would be 4 hours * $17.50/hour = $70.
Next, we determine the amount of income tax. Dylan's income tax rate is 15%, so he would pay 15% of his total earnings in taxes: 15/100 * $70 = $10.50 in taxes.
Finally, we calculate Dylan's net earnings after tax by subtracting the tax amount from his total earnings: $70 - $10.50 = $59.50. Therefore, Dylan will earn $59.50 after taxes for 4 hours of work.
Learn more about Income Tax Calculation here:https://brainly.com/question/34135935
#SPJ12
Dylan earns $59.50 after taxes.
Explanation:To calculate the amount Dylan earns after taxes, we need to first find out his total earnings before taxes.
Dylan works for 4 hours and is paid $17.50 per hour, so his total earnings before taxes are 4 hours multiplied by $17.50, which is $70.
Next, we need to calculate the amount of income tax Dylan needs to pay. He must pay 15% of his total earnings as income taxes, which is 15% of $70, which is $10.50.
To find out how much Dylan earns after taxes, we subtract the income tax amount from his total earnings,
so $70 - $10.50 = $59.50.
Therefore, Dylan earns $59.50 after taxes.
Learn more about Calculating Earnings after Taxes here:
https://brainly.com/question/33832255
#SPJ12
You choose at random from letters a,b,c, and d, and you roll a number cube once. What are your chances you get a and 5
Answer:
your answer is 10! please mark brainliest :))))))
Step-by-step explanation:
Two cylinders, a and b are created cylinder a has volume v culinder b has the same height as a cylinder be has half the width of cylinder a write an expression that represents the volume of cylinder b in terms of v
Answer:
v/4
Step-by-step explanation:
Volume of cylinder a = v
Let the height of cylinder a is h and its radius is r. The volume of cylinder a will be:
[tex]v=\pi r^{2}h[/tex]
Height of cylinder b is same as cylinder a. So height of cylinder b is h.
Radius of cylinder b is half of radius(width) of cylinder a. So radius of cylinder b will be r/2
The volume of cylinder b will be:
[tex]v^{'}=\pi (\frac{r}{2} )^{2}h\\\\ v^{'}=\pi(\frac{r^{2}}{4})h \\\\ v^{'}=\frac{\pi r^{2}h}{4} \\\\ v^{'} = \frac{v}{4}[/tex]
Thus the volume of cylinder b will be v/4
Answer:
The volume of cylinder A is four times the volume of cylinder B.
Step-by-step explanation:
count me brainliest
In london, 1 litre of petrol costs 108.9p In Ney York, 1 US gallon of petrol costs $2.83 1 US gallon = 3.785 litres ?1= $1.46 In which city is petrol better value for money, London or New York? You must show your working.
Answer:
In London it cost $ 6.017 while in Newyork it cost $2.831
so NewYork is cheaper
Step-by-step explanation:
As we know, 1 US gallon = 3.785 liters
so,converting liters into gallon = 1.089 * 3.785
= 4.121 per gallon
Cost of 4.121 gallon petrol in dollars = 4.121 * 1.46
= $ 6.017
In London it cost $ 6.017 while in Newyork it cost $2.831
so NewYork is cheaper
Final answer:
Petrol is better value for money in New York, where it costs approximately £0.512 per litre after converting from USD to GBP and gallons to litres, compared to £1.089 per litre in London.
Explanation:
To determine where petrol is better value for money, we need to compare the cost per litre in both London and New York, taking into account the exchange rate and units of measure. First, let's convert the cost of petrol in New York from gallons to litres:
The cost of 1 US gallon of petrol in New York is $2.83.1 US gallon is equivalent to 3.785 litres. So to find the cost per litre we divide $2.83 by 3.785 litres: $2.83 / 3.785 litres = $0.748 per litre.Next, we'll convert the cost from dollars to pounds using the given exchange rate of £1 = $1.46. So $0.748 multiplied by the exchange rate: $0.748 / $1.46 = £0.512 per litre.Now, let's compare it to the cost in London:
The cost of petrol in London is 108.9p per litre, which is equivalent to £1.089 per litre.Comparing the two:
London: £1.089 per litreNew York: £0.512 per litreTherefore, the petrol is better value for money in New York as £0.512 per litre is less than £1.089 per litre.
The angle of elevation from a soccer ball on the ground to the top of the goal is 38 degrees. If the goal is 8 feet tall, what is the distance from the ball to the goal?
Answer:
The distance is 10.24 feet ( to the nearest hundredth).
Step-by-step explanation:
Use trigonometry of a right angled triangle:
The angle = 38 degrees, opposite side = 8 ft, we require the adjacent side: We have opposite / adjacent side so we need the tangent.
tan 38 = 8 / a
a = 8 / tan 38
= 10.24 feet.
All of the angles are exterior angles EXCEPT:
Answer:
Step-by-step explanation:
XYZ
The first one
I hope I helped you.
Can someone please help me with this?
Answer:
23
Step-by-step explanation:
angles in a triangle add up to 180 so
124+33=157
180-157=23
x=23
y is 23 as well and z is 124
Suppose x has a distribution with μ = 40 and σ = 12. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μ x = 40 and σ x = 0.8. Yes, the x distribution is normal with mean μ x = 40 and σ x = 12. Yes, the x distribution is normal with mean μ x = 40 and σ x = 3. No, the sample size is too small. Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 40 and σ x = 3. Yes, the x distribution is normal with mean μ x = 40 and σ x = 12. Yes, the x distribution is normal with mean μ x = 40 and σ x = 0.8.
Answer:
a: no the sample size is too small
b: Yes, the distribution is normal with a mean of 40 and standard deviation of 12
Step-by-step explanation:
a: If n < 30, we need to know that the sample is normally distributed or else we can't determine anything. When sample sized get very large, they usually resemble normally distributed data sets so we can still make conjectures even if the data isn't officially normally distributed
b: The question tells us that the sample is normally distributed, so even though n < 30, we can still make conjectures about the population
In the figure, is tangent to the circle at point U. Use the figure to answer the question.
Describe the relationship among the lengths of the segments formed by the secant RT, and the tangent Suppose RT=16 in. and ST=4 in. Find the length of . Show your work.
Answer:
The length of TU is [tex]8\ in[/tex]
Step-by-step explanation:
we know that
The Intersecting Secant-Tangent Theorem states that, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
in this problem
[tex]TU^{2}=RT*ST[/tex]
we have
[tex]RT=16\ in[/tex]
[tex]ST=4\ in[/tex]
[tex]TU^{2}=(16)(4)[/tex]
[tex]TU^{2}=64[/tex]
[tex]TU=8\ in[/tex]
Use the limit theorem and the properties of limits to find the limit.
Answer:
The answer is √3/4 ⇒ answer (d)
Step-by-step explanation:
∵ [tex]\lim_{n \to \infty} \frac{\sqrt{3x^{2}+2} }{4x+1}[/tex]
* By using the limit theorem: divide up and down by x
∵ x = √x²
∴ [tex]\sqrt{\frac{3x^{2} }{x^{2}}+\frac{2}{x^{2}}[/tex] =
[tex]\sqrt{3+\frac{2}{x^{2}}[/tex] ⇒ numerator
∵ [tex]\frac{4x}{x}+\frac{1}{x}=4+\frac{1}{x}[/tex] ⇒ denominator
∵ x →∞ ⇒ ∴ 2/x² = 2/∞ = 0 and 1/x = 1/∞ = 0
∴ [tex]\lim_{x \to \infty}\frac{\sqrt{3+\frac{2}{x^{2}}}}{4+\frac{1}{x}}=\frac{\sqrt{3}}{4}[/tex]
∴ The answer is √3/4 ⇒ (d)
The answer is: [tex]d.\frac{\sqrt{3} }{4}[/tex]
Why?Since the degree of both numerator and denominator are the same, the result will be a number different of zero, so the first given option (a) it's incorrect.
We need to "break" the indeterminate form of the limit in order to find the correct answer.
To solve this limit, we must divide each term by the largest degree term, for this case is "x" since the numerator is inside of a square root.
So, doing it we can solve the limit:
[tex]\lim_{x \to \infty}\frac{\sqrt{\frac{3x^{2} }{x^{2} }+\frac{2}{x^{2}}}}{\frac{4x}{x}+\frac{1}{x}}\\\\ \lim_{x \to \infty} \frac{\sqrt{3+\frac{2}{x^{2}}}}{4+\frac{1}{x}}[/tex]
Then, before evaluating the limit, we must remember that any number divided by infinity will give as result zero (0), so:
[tex]\lim_{x \to \infty} \frac{\sqrt{3+\frac{2}{(infinity)^{2}}}}{4+\frac{1}{infinity}}\\\\\lim_{x \to \infty} \frac{\sqrt{3+0}}{4+0}=\frac{\sqrt{3} }{4}[/tex]
So, the correct option is: [tex]d.\frac{\sqrt{3} }{4}[/tex]
Have a nice day!
What is the sum of the first 19 terms of the arithmetic series?
3+8+13+18+…
Enter your answer in the box.
_______
Answer:
i think its 912
Step-by-step explanation:
i am not sure though
The sum of the first 19 terms of the given arithmetic series is equal to 912.
Given the following sequence:
3 + 8 + 13 + 18 + …What is an arithmetic series?A arithmetic series can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
Mathematically, an arithmetic series is given by the expression:
[tex]S_n = \frac{n}{2}(2a +(n-1)d)[/tex]
Where:
d is the common difference.a is the first term of an arithmetic series.n is the total number of terms.Substituting the given parameters into the formula, we have;
[tex]S_{19} = \frac{19}{2}(2(3) +(19-1)5)\\\\S_{19} = 9.5(6+18(5))\\\\S_{19} = 9.5(6+90)\\\\S_{19} = 9.5 \times 96[/tex]
19 term = 912.
Read more on arithmetic series here: brainly.com/question/12630565
Use the graph of the function f to determine the given limit
Answer: b. 3
Step-by-step explanation:
The limit of the function as it approaches -3 from the left is 3.
The limit of the function as it approaches -3 from the right is 3.
Since the limit from the left equals limit from the right, then the limit of the function exists and is 3.
Answer: 3, or b
Step-by-step explanation:
The rule that it comes from both the right and the left and meets at a common point verifies this.
What is the equation of a circle whose center is begin ordered pair negative 4 comma 6 end ordered pair and whose radius is 9 cm? Question 1 options: open parentheses x minus 4 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 81 open parentheses x plus 4 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 3 open parentheses x plus 4 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 81 open parentheses x minus 4 close parentheses squared plus open parentheses y plus 6 close parentheses squared equals 3
Answer:
[tex](x+4)^2+(y-6)^2=81[/tex]
Step-by-step explanation:
We want to find equation of a circle with center (-4,6) and radius 9cm.
The equation of a circle with center (h,k) and radius [tex]r[/tex] units is given by;
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We substitute the radius and the center to obtain;
[tex](x+4)^2+(y-6)^2=9^2[/tex]
The required equation is:
[tex](x+4)^2+(y-6)^2=81[/tex]
The value of y varies directly with x, when x=1/4, y=25. What is the value of y when x= 2 1/3
The value of y, when x = 2 1/3 in a direct variation scenario where y = kx (k being the constant of variation), is approximately 233.3.
Explanation:In the given problem, the value of y varies directly with x. This means there's a constant of variation, k, such that y = kx. We can find k by plugging in the initial given values, x=1/4 and y=25, into this equation, which gives us k = y/x = 25/(1/4) = 100.
Now that we know k, we can calculate the value of y when x = 2 1/3 using the same equation. Here, y = kx = 100 * 2 1/3 = 100 * 7/3 = 700/3 = 233.3 recurring.
So, when x = 2 1/3, y is approximately 233.3.
Learn more about Direct Variation here:https://brainly.com/question/9775007
#SPJ12
When [tex]\(x = \frac{1}{4}\), \(y = 25\)[/tex] in a direct variation relationship. The constant of variation[tex](\(k\))[/tex] is found to be 100. Thus, when[tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]
If the value of [tex]\(y\)[/tex] varies directly with[tex]\(x\),[/tex] we can express this relationship using the formula [tex]\(y = kx\),[/tex] where [tex]\(k\)[/tex] is the constant of variation.
Given that when [tex]\(x = \frac{1}{4}\), \(y = 25\),[/tex] we can use this information to find [tex]\(k\)[/tex]:
[tex]\[25 = k \times \frac{1}{4}\][/tex]
Solving for [tex]\(k\):[/tex]
[tex]\[k = 25 \times 4 = 100\][/tex]
Now that we know [tex]\(k = 100\),[/tex] we can find the value of[tex]\(y\)[/tex] when[tex]\(x = 2 \frac{1}{3}\)\\[/tex]
[tex]\[y = 100 \times 2 \frac{1}{3} = 100 \times \frac{7}{3} = \frac{700}{3}\][/tex]
Therefore, when [tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]
Use the laws of logarithms and the values given below to evaluate the logarithmic expression (picture provided)
Answer: Option a.
Step-by-step explanation:
To solve the given exercise, you must keep on mind the law of logarithms shown below:
[tex]log(a)-log(b)=log(\frac{a}{b})[/tex]
Therefore, by applying the law , you can rewrite the expression given, as following:
[tex]log(\frac{5}{7})=log(5)-log(7)[/tex]
You know that:
[tex]log5=0.6990\\log7=0.8451[/tex]
Then, when you substitute values, you obtain:
[tex]0.6990-0.8451=-0.1461[/tex]
Use the quotient rule [ [tex]\text{log}_a\frac{x}{y} = \text{log}_ax-\text{log}_ay[/tex] ] to simplify.
[tex]\text{log}\frac{5}{7} = \text{log}(5)-\text{log}(7)[/tex]
Simplify using the given values.
0.6990 - 0.8451
-0.1461
Therefore, [tex]\text{log}\frac{5}{7}=-0.1461[/tex]
Best of Luck!