Answers
Answer:
\(\log_{10}2=0.3010\)
Step-by-step explanation:
\(a^c=b \implies \log_ab=c\)
Given: \(2=10^{0.3010}\)
Therefore,
a = 10b = 2c = 0.3010\(10^{0.3010}=2 \implies \log_{10}2=0.3010\)
Related Questions
Use the graph of y=f(x) in the figure to estimate:
f(0)≈
f(1)≈
f(b)≈
f(c)≈
f(d)≈
Answers
9514 1404 393
Answer:
f(0) ≈ 22f(1) = 10f(b) ≈ -8f(c) = 0f(d) 24Step-by-step explanation:
This takes graph-reading one step further. You get to estimate the y-value without benefit of minor grid lines. You must mentally divide the 10-unit distance between grid lines into equal spaces. Then estimate how many of those spaces lie between the point and the nearest grid line.
You can do this more precisely by drawing a diagonal line across the grid from one major grid intersection to one that is (5, 1) or (5, -1) major grid points away. Where that line crosses the intermediate grid lines, the vertical measure will be some multiple of 1/5 of the vertical difference between grid points. For example, a line from (0,20) to (5,30) will cross at (1,22), (2,24), (3,26), and (4,28). You can use these reference points to identify the y-values at f(0) and f(d).
Here's our eyeball estimate:
f(0) ≈ 22f(1) = 10f(b) ≈ -8f(c) = 0f(d) 24
Cómo se hace y cómo es el proceso ayuda porfaaaaa
Answers
Answer:
30: 100
31: -13
32: -45
33: 14
34: -32
35: -22
36: 17
Need help with this geometry question.What is HK?
Answers
Answer:
Step-by-step explanation:
use a protractor if you have one or ask for one
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
13 ft
5 ft
?
9 ft
6 ft
4 ft
Answers
The measure of the missing side length from the given figure is 11 feet.
What is right angle?The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection.
It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.
The adjacent angles are right angles if a ray is positioned so that its terminus is on a line and they are equal.
In the given figure, assuming that all the intersecting sides meet at right angles.
So, the opposite sides are parallel to each other.
Let x be the length of missing side.
Thus, The length of missing side = Sum of length of parallel sides
Now, x= 5+6
= 11 feet
Therefore, the length of side missing is 11 feet.
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Not drawn
accurately
A
B
The perimeter of Shape A is 72cm. What is the perimeter
of Shape B?
Answers
John left the museum and drove south at a rate of 55 mph. Sally left four hours later driving 10 mph faster than John in an effort to catch up to him. How
long did Sally have to drive to catch up with John?
28 hours
22 hours
20 hours
18 hours
Answers
Answer:
22 hours (B)
Step-by-step explanation:
John's velocity = 55mph
Sally's velocity = 65mph
John's time taken = x
Sally's time taken = x - 4
since they must cover the same distance.
and, distance = vel × time
Sally's vel × time = John's vel × time
55x = 65(x-4)
55x = 65x - 220
-10x = -220
x = 22 hours.
Therefore, Sally catches up after 22 hours
1. The possible missing terms to make x²_____+100 a perfect square trinomial are
a. 4x and 25x.
b. -10x and 10x.
c. -20x and 20x.
d. -4x and -25x.
Answers
Answer:
c. -20x and 20x
Step-by-step explanation:
x² is the square of x.
100 is the square of 10 and of -10.
The middle term of (a + b)² is 2ab.
For b = 10:
2ab = 20x
for b = -10:
2ab = -20x
Answer: c. -20x and 20x
Certain advertisers would like to estimate the proportion of viewers who spend the majority of their television time
watching alone. The consensus is that this percentage has been increasing over the years due to the increased
number of television sets in households.
a. Determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than
6% to estimate the true proportion of viewers who watch television alone.
b. What impact would a pilot sample that showed that 44% of viewers spend the majority of their television time
watching alone have on your on results.
a. The sample size needed is
(Round up to the nearest integer.)
b. The new sample size needed would be 0
(Round up to the nearest integer.)
Answers
Answer:
Step-by-step explanation:
(help pls 25 points) To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Answers
Answer:
Step-by-step explanation:
4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Answer: c and E
Step-by-step explanation:
An isosceles triangle whose sides are 5cm, 5cm and 6cm is inscribed in a circle. Find the radius of the circle.
Answers
Answer:
To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:
r = (a/2) * cot(π/n)
where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.
In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:
6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)
36 = 50 - 50cos(x)
cos(x) = (50 - 36)/50
cos(x) = 0.28
x = cos^-1(0.28) ≈ 73.7°
Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:
(5/2)^2 + h^2 = 5^2
25/4 + h^2 = 25
h^2 = 75/4
h = sqrt(75)/2 = (5/2)sqrt(3)
Now we can find the radius of the inscribed circle using the formula:
r = (a/2) * cot(π/n)
where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:
r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm
Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.
what's an isosceles triangle; triangle with 2 equal sides; area of isosceles triangle
Answers
The length of 2 sides and an angle between them is given A = ½ × b × c × sin(α) If two angles and the length between them is given A = For an isosceles right triangle A = ½ × a.
How big is an isosceles triangle?
If the height (i.e. the altitude) and base of an isosceles triangle are known, the area can be easily calculated. The area of the isosceles triangle is calculated by multiplying the height by the base and dividing by two. As a result, an isosceles triangle has two equal sides and two equal angles. The name is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.
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Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)
Answers
Answer:
\({ \bf{f(x) = \tan x + 9 \sin x }}\)
For gradient, differentiate f(x):
\({ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}\)
Substitute for x as π:
\({ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}\)
Gradient of tangent = -8
\({ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi\)
Equation of tangent:
\({ \boxed{ \bf{y = - 8x + 8\pi}}}\)
PLEASE HELP 20 POINTS!
Answers
Answer:
WHAT PERCENT?
FOR ME IS B. 20%!HOPE THIS HELPS YOU ANSWER :)
#CarryOnLearning!
There are 616 calories in eight ounces of a certain ice cream. How many calories are there in one pound?
Answers
Answer 1232
Step-by-step explanation:
16 oncues equal 1 pound so 8x2 equals 16
so you would moultiply 616x2
Answer: 1,232 calories
Step-by-step explanation: Since there’s 16 ounces in a pound, all you have to do is multiply 616 by 2 which equals 1,232 calories. 8 times 2 = 16, so 616 times 2 = 1,232
Determine the domain of each relation, and determine whether each relation describes y as a function of b, x = b
Answers
The Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.
Explain about the domain of the function?X is equal to why's absolute value, and we're looking for the domain. Remember that the domain is simply the set of all conceivable X values. As a result, when we look at the this equation, an absolute value sign just on y axis makes all negative numbers positive and all positive numbers, just that one number, positive.For the stated question:
Relation : x = b
Its absolute value of a negative is equal to the absolute amount of a positive alone.
Since zero's absolute value was only zero, all of the X values has to be positive or zero. Because if an exit value had a negative value, the absolute value sign could be in contravention of its rule.Therefore, the domain includes only positive numbers plus zero, and we can use any value for X to check whether or not it is a function. Let's assume that X is 20. 20 equals are available. the reason in its entirety Since we just observed that absolute value of the a negative number up above, y in this case may either equal only positive 20 and y can equal negative 20. This case's negative 20 is only 20, after all.Thus, the Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.
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Linda is making curtains . She has 2 1/3 yards of material . She wants to make 3 curtains . She needs 8/9 yard for each curtain . Does she have enough material for 3 curtains?
Answers
======================================================
Use this formula
a & b/c = (a*c + b)/c
to convert from a mixed number to an improper fraction.
Let's use that formula to find the following
a & b/c = (a*c + b)/c
2 & 1/3 = (2*3+1)/3
2 & 1/3 = 7/3
She has 7/3 yards of material.
Linda wants to make 3 curtains. Each curtain needs 8/9 of a yard.
3*(8/9) = 24/9 = (8*3)/(3*3) = 8/3
Therefore, she needs 8/3 yards of material.
But this is a problem because she needs more material than what she has on hand. In other words, 8/3 > 7/3 since 8 > 7.
-----------
Another way to look at it:
7/3 = 2.333 yards is the approximate amount of fabric she has
8/3 = 2.667 approximately is the total amount of fabric she needs, which is clearly larger than the 2.333 yards she has.
Unfortunately Linda does not have enough fabric to make 3 curtains.
Find the slop of the lineWrite answer as an integer or a reduced fraction. Do NOT use 1 as a denominator!
Answers
Solution:
To get the slope of a line from a given graph, the coordinates of any two clear points are chosen.
From the graph given, pick the points (4,0) and (8,8).
\(\begin{gathered} \text{where;} \\ x_1=4 \\ y_1=0 \\ x_2=8 \\ y_2=8 \end{gathered}\)The formula for calculating the slope of a line, m is given by;
\(m=\frac{y_2-y_1}{x_2-x_1}\)Substituting the coordinates into the formula,
\(\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{8-0}{8-4} \\ m=\frac{8}{4} \\ m=2 \end{gathered}\)Therefore, the slope of the line is 2.
A right rectangular prism has the dimensions 4 by 6 by 3 feet. Enter the volume, in cubic feet, of the rectangular prism.
Answers
Explanation: volume= length x width x height
Therefore 4x6x3=72 cubic feet
factorise x³-4x²+x+6
Answers
The binomial factors of x³- 4x²+x+6 are (x+2), (x+3), and (x-1).
Using the splitting and grouping the terms:
x³ + 4x² + x - 6
= x³ + 2x² + 2x² + x - 6 [Splitting 4x² = 2x² + 2x²]
= (x³ + 2x²) + (2x² + x - 6)
= x² (x + 2) + (2x² + 4x - 3x - 6)
= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]
= x² (x + 2) + (x + 2) (2x - 3)
= (x + 2) ( x² + 2x - 3)
= (x + 2) ( x² + 3x - x - 3)
= (x + 2) [x (x + 3) - 1 (x + 3)]
= (x + 2) (x + 3) (x - 1)
Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)
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secure admin 171 acellus.com st
are Roots and the Pythagorean Theorem
10 in a
Find the length of b.
Hint: a² + b² = c²
15 in
b
[?] in
Round your answer
to the nearest tenth.
b = [?] in.
USE A
Enter
Answers
Applying the Pythagοrean theοrem, the length οf b, tο the nearest tenth, is 11.2.
What is the Pythagοrean theοrem in mathematics?Pythagοras' theοrem states that a right triangle's hypοtenuse square must be equal tο the sum οf its twο οther side squares.
The hypοtenuse οf a right triangle, which is οften its lοngest leg, can be calculated using the Pythagοrean theοrem by applying the fοrmula a²+b² = c². The triangle's sides a and b are the twο "nοn-hypοtenuse" sides.
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is 11.2.
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Complete reference question:
What information would you need to prove that these two triangles were congruent using the: HL Theorem?
Answers
Answer:
I forget about these theorems and such, but pretty sure this is the Hypotenuse - Leg congruence theorem.
Step-by-step explanation:
As the name infers, you need the length hypotenuse and the length of one leg of each triangle. This is because you can use Pythagorean to find the last side, turning it into SSS congruence theorem. You also need them both to be right triangles for pythag to work.
Answer:what 2 triangles
Step-by-step explanation:Happy new year btw
The table below shows how many millilitres are on different numbers of liters Mark all of the true statements
Answers
the only true statement is
in 4 liters there are 4000 milliliters
jenni wrote a rational number that is positive which of the following us not a possible number she wrote? a. 0 b. 1 c. 7/8 d . 5 1/4
Answers
What is the slope of a line perpendicular to the line whose equation is 4x-3y=-3 simple answer
Answers
Answer:
3=-4x+3y or -4x+3y=3
Step-by-step explanation:
it perpendicular
Slope of the line,
4x - 3y = -3
Or, 3y = 4x + 3
y = (4x + 3)/3
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8.
a. What is the probability that a student scored below 91 on this exam?
b. What is the probability that a student scored between 65 and 89?
c. If the professor grades on a curve (i.e., gives A’s to the top 10% of the class, regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam, where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain. (Hint: For option 1, you need to find a minimum Z-score that will guarantee you that you will be in the top 10% of the class.)
Answers
a. The probability that a student scored below 91 on this exam is 0.9878
b. The probability that a student scored between 65 and 89 is 0.8186.
c. A grade of 68 on the second exam is better than a grade of 81 on the first exam for the given conditions
a. To find the probability that a student scored below 91 on the exam, we need to find the area under the normal distribution curve to the left of 91. Using a standard normal distribution table or calculator, we can find the corresponding Z-score as:
Z = (91 - 73) / 8 = 2.25
The probability of scoring below 91 is then the same as the probability of a standard normal random variable being less than 2.25, which is approximately 0.9878.
b. To find the probability that a student scored between 65 and 89, we need to find the area under the normal distribution curve between these two values. Using the Z-score formula as above, we find:
Z1 = (65 - 73) / 8 = -1.00
Z2 = (89 - 73) / 8 = 2.00
Using a standard normal distribution table or calculator, we can find the probability of a standard normal random variable being between -1.00 and 2.00, which is approximately 0.8186.
c. To determine if a grade of 81 on this exam or a grade of 68 on a different exam is better if the professor grades on a curve, we need to find the Z-score that corresponds to the top 10% of the class. Using a standard normal distribution table or calculator, we can find this Z-score as:
Z = 1.28 (approximately)
For the first exam, the Z-score corresponding to a grade of 81 is:
Z = (81 - 73) / 8 = 1.00
Since 1.00 < 1.28, a grade of 81 is not in the top 10% of the class. For the second exam, the Z-score corresponding to a grade of 68 is:
Z = (68 - 62) / 3 = 2.00
Since 2.00 > 1.28, a grade of 68 is in the top 10% of the class. Therefore, if the professor grades on a curve, a grade of 68 on the second exam is better than a grade of 81 on the first exam.
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What inequality represents all the values of x for y <
-5(x - 8) - 2 when y = 7?
Answers
Answer:
(−∞, 31/5) or x <31/5 (the graph will start a little bit past 6 and will be a open circle and head to the left)
Answer:
x< 6\(\frac{1}{5}\)
Step-by-step explanation:
7<-5(x -8) - 2 Distribute the 5
7<-5x + 40 - 2
7<-5x +38 Subtract 38 from both sides
-31<-5x Divide both sides by -5
\(\frac{31}{5}\) >x When you divide both sides by a negative number, you must flip the sign.
or
x < 6 \(\frac{1}{5}\)
the algebric expression of substrabing 4x from the square root of y is?
(1)
\( \sqrt{y} - 4x\)
2.
\(4x - \sqrt{y} \)
3.
\( {y}^{2} - 4x\)
4.
\(4x - {y}^{2} \)
Answers
\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)
The algebric expression of substrabing 4x from the square root of y is?
1. \(\tt \sqrt{y} - 4x\)
2. \(\tt4x - \sqrt{y} \)
3. \(\tt {y}^{2} - 4x\)
4. \(\tt4x - {y}^{2} \)
\( \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}\)
Here, we have the keyword ⇨ subtracting 4x from the square root of y.Since, there's the word 'from', we must put the square root of y first, then add the minus symbol since the operation given is subtraction & lastly, we should add 4x.This is how you write the square root of y \(\downarrow\)\( \large \tt \sqrt{y} \)The last 2 options show y² (y to the power of 2 / y square).... it's not the square root of y. So, we can eliminate the last 2 options.Now, let's identify the correct answer from the 1st 2 options. I already explained that the square root of y should come first, so the correct answer is Option 1. \(\boxed{\boxed{\bf \sqrt{y} - 4x}}\)A rectangular prism with a base that is
5 inches by 4 inches and a height of 15 inches.
Answers
The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
V = a × b × c unit³
The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]
= 310 inches²
The volume of the prism = 5 × 4 × 15
= 300 in³
Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
The complete question is:
A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?
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Help please its math triangles..
Answers
Answer:
28
Step-by-step explanation:
Add the top and bottom bases, divide by 2, multiply by height.
PLEASE HELP FAST. Maggie pays for a 6-month subscription to a video streaming channel. Because she purchased 6 months at once, she receives a $10 discount. Her final price after the discount is $43.94. What was the original price per month (H)?
Answers
Answer:
53.94$
Step-by-step explanation:
Answer:
53.94$
Step-by-step explanation: