Answers
Answer:
D) 0.69
Step-by-step explanation:
Given :
5 × 2³ˣ = 21
Divide by 5 on each side :
1/5 x 5 x 2³ˣ = 1/5 x 212³ˣ = 4.2Taking the cubic root :
∛2³ˣ = ∛4.22ˣ = 1.61Using logarithm values :
log(2ˣ) = log(1.61)x log(2) = log(1.61)x = log (1.61) / log (2)x = log₂ (1.61)x = 0.69 (approximately)Answer:
D. 0.69
Step-by-step explanation:
Given equation:
[tex]5 \cdot 2^{3x}=21[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{5 \cdot 2^{3x}}{5}=\dfrac{21}{5}[/tex]
[tex]\implies2^{3x}=4.2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies(2^3)^x=4.2[/tex]
[tex]\implies8^x=4.2[/tex]
Take natural logs of both sides:
[tex]\implies \ln 8^x=\ln 4.2[/tex]
[tex]\textsf{Apply the log Power law} \quad \ln x^n=n\ln x :[/tex]
[tex]\implies x \ln 8=\ln 4.2[/tex]
Divide both sides by ln 8:
[tex]\implies \dfrac{x \ln 8}{\ln 8}=\dfrac{\ln 4.2}{\ln 8}[/tex]
[tex]\implies x=\dfrac{\ln 4.2}{\ln 8}[/tex]
[tex]\implies x=0.690129776...[/tex]
[tex]\implies x=0.69 \: \sf (2\:dp)[/tex]
Related Questions
NEED HELP ASAP - Which
represents the inverse of the function f(x) = 4x?
h(x) = x + 4
• h(x) =x-4
h(x) = =3/4x
O h(x) = 1/4
Answers
Answer:
O h(x)=1/4
Step-by-step explanation:
You wish to test the following claim (
H
a
) at a significance level of
α
=
0.002
.
H
o
:
μ
=
63.5
H
a
:
μ
<
63.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size
n
=
62
with mean
M
=
56.3
and a standard deviation of
S
D
=
13.2
.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Answers
Using the t-distribution, it is found that the desired measures are given as follows:
The test statistic is t = -4.29.The p-value is of 0.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 63.5, that is:
[tex]H_0: \mu = 63.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:
[tex]H_1: \mu < 63.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]
t = -4.29.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.
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Oliver completed his project in no more than twice the amount of time it took Karissa to complete her project. Oliver spent 4 and one-fourth hours on his project. If k represents the amount of time that it took Karissa to complete her project, which inequality can be used to represent the situation?
4 and one-fourth less-than 2 k
4 and one-fourth less-than-or-equal-to 2 k
4 and one-fourth greater-than 2 k
4 and one-fourth greater-than-or-equal-to 2 k
Answers
Answer:
4 and one-fourth less-than or equal-to 2k
Step-by-step explanation:
4 and one-fourth is no more than 2k
i.e,4 and one-fourth can be equal or less than 2k
pls mark brainliest:)
Maya has savings of $40,000. She invests in a bond mutual fund that pays 5% interest each year. Ignoring compounding, what are Maya's total savings after 20 years?
Answers
Answer:50,000 x 0.04 x 20=40,000
The total saving after 20 years 50,000+40,000=90,000$
What is the area of this rectangle?
18 m
9 m
14 sq m
16 sq m
Answers
Answer:
14
A = base × height = 2 × 7 = 14
Answer:14
Step-by-step explanation:
A submarine starts 15 meters above sea level and travels 95 meters below sea level. How far did the submarine travel? *
Answers
The height attained by the submarine in the sea will be 80 meters.
What is the height?
Height is a vertical distance travelled by any object. Here the submarine is going down in the sea from 15 meters to 95 meters below the sea.
So the height attained by the submarine will be:-
H= 95-15
H= 80 meters.
Therefore the height attained by the submarine in the sea will be 80 meters.
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share the ration .....
Answers
Answer:
Tom: £166
Ben: £581
Step-by-step explanation:
In the ratio 2 : 7 there are 9 portions total (2 + 7 = 9).
£747 / 9 = £83
For Tom:
£83 * 2 = £166
For Ben:
£83 * 7 = £581
Checking our work:
Since the decimals are the same, this means the ratios are equal.
2/7 = 0.2857
166/581 = 0.2857
The Ferris wheel at the museum park has a height requirement of 48 inches your little sister is 45 inches tall how much taller does she need to go before she can ride the Ferris wheel
Answers
Answer:
3 inches
Step-by-step explanation:
48 - 45 = 3
Help. Please and thanks
Answers
Step-by-step explanation:
24.
AC = 12 = cos(angle) × AB = cos(angle) × 13
imagine a circle with center in A and radius 13.
that is why we can say AC = cos(angle) × radius, and BC = sin(angle) × radius.
cos(angle) = 12/13 = 0.923076923...
angle = 22.61986495...°
so, B is the right answer.
25.
we have a right-angled triangle.
from the point in the ground, where the ladder starts, to the point on the wall, where the ladder ends, and the point on the ground right under the wall point.
at this ground point there is the right angle.
at the ladder ground point we have 70°.
so, the angle at ladder/wall point is
180 - 90 - 70 = 20°.
remember, the sum of all angles in a triangle is always 180°.
the ladder itself (20 ft) is the Hypotenuse (the baseline opposite of the 90° angle).
the height of the ladder/wall point is one leg (and what we need to calculate), and the ground distance from the ladder/ground point to the point right under the ladder/wall point is the second leg.
we can use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being always opposite of the associated angles.
so, we have
20/sin(90) = 20/1 = 20 = height/sin(70)
height = 20×sin(70) = 18.79385242... ft
so, D is the right answer.
Is 2/3 < 3/4 , or is 3/4 < 2/3 ? Explain how you know.
Answers
Answer:2/3 < 3/4
Step-by-step explanation: 3/4 is greater than 2/3.
On a number line 1.77 would be located where?
Answers
Step-by-step explanation:
1.77 would be closer to 2
look at the attachment and solve
Answers
The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.
What is a perpendicular bisector?A perpendicular bisector of a line segment is a line segment that is perpendicular to and passes through the middle of the line segment (left figure). A line segment's perpendicular bisector can be drawn using a compass by drawing circles centred at and with radius and connecting their two intersections.
The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.
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Given that A, O & B lie on a straight line segment, evaluate obtuse ∠AOC.
The diagram is not drawn to scale.
∠AOC=
Answers
Answer:
AOC = 124°
Step-by-step explanation:
Angle on a straight line is 180°, therefore, the sum of the three angles shown is 180;
This can be written like so:
(3x + 94) + (x + 30) + (2x - 4) = 180
This equation can be solved to find x:
6x + 120 = 180
6x = 180 - 120
6x = 60
x = 10
AOC = 3(10) + 94
= 30 + 94
= 124
Answer:
angle AOC = 124
Step-by-step explanation:
3x + 94 + x + 30 + 2x - 4 = 180 ( ^'s on a STR line)
6x = 180 - 120
6x = 60
x = 10
sub x into 3x + 94
3(10) + 94 = 124
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
The answer to writing this graph in fully simplified slope-intercwpt form is y = 1/5x - 7.
30 POINTS. HELP!
Which of the three types of discontinuities (removable, jump, and infinite), would be represented by a limit that can only be found by simplifying a rational expression or multiplying by a conjugate? Why?
Answers
Answer:
jump equation
bu multiplying by a conjugate
What is the circumference of the circle? (use 3.14 for pi)
(WORTH 30 POINTS)
Answers
Answer:
119.32
Step-by-step explanation:
[tex]A = 2 * 3.14 * 19 = 119.32[/tex]
can anyone help me identify the center and radius on these 3 pls , brainly
Answers
Radius = r^2 = 225 => r = 15
b)center is (0,0)
Radius r^2= 178
=> r =13.34
C) center is (0,0)
Radius is r^2 = 49 => r = 7
Hope it helps .
Answer:
Note that #1 starts at #3 and #3 on this list ends at #5 on your page.
Center, 0 | Radius, 15Center, 0 | Radius, [tex]\sqrt{178}[/tex]Center, 0 | Radius, 73) A customer in a bookstore is interested in eleven books on sale.
How many ways can she select three books to buy?
Answers
33
Step-by-step explanation:
This is a simple probability question so you do 11x3 for example you have a 4 shirts and 4 shoes you can make 16 different outfits.
Help me plsssssssssssss
Answers
Answer:
3/1/4
That's the expression represents Lena's speed in miles per hour
Tom would like to stock groceries for his shop. The wholesaler where he buys his stock sells sugar in packets of 10 per carton, flour in packets of 6 per carton and rice in packets of 5 per carton. How many cartons of each item should Tom buy so that there are equal number of packets of sugar, flour and rice.
Answers
Answer: Sugar = 3 cartons, Flour = 5 cartons, Rice = 6 cartons
Step-by-step explanation:
Sugar = 10 packets/carton
Flour = 6 packets/carton
Rice = 5 packets/carton
10, 20 30... sugar
6, 12, 18, 24, 30... flour
5, 10, 15, 20, 25, 30... rice
30/10 = 3 cartons of sugar
30/6 = 5 cartons of flour
30/5 = 6 cartons of rice
For all the number of packets to be equal.
flour cartons, 5
rice cartons, 6
Find any 2 irrational no. Between 0.1 and 0.12
Answers
0.10100100010000 and 0.110100100010000 are two irrational numbers between 0.1 and 0.12.
Step-by-step explanation:
Any two irrational Numbers between 0.1 and 0.12 will be those numbers which will be=> greater than 0.1 and smaller than 0.12
And those numbers are = 0.10100100010000 and 0.110100100010000.You can also choose any other numbers too.
___________________Irrational Number :
Irrational numbers are non terminatingNon recurring / repeating✓ Be sure your photo is not blurry
7x-3(5x+2)-6(7+2x)
Answers
Answer:
-20x-48
Step-by-step explanation:
7x-(15x +6)-6(7+2x)
7x-(15x+6)-(42+12x)
7x-15x-6-42-12x
(7x -15x-12x)+(-6-42)
=-20x-48
Answer:
-20x - 48
Step-by-step explanation:
7x - 3(5x +2) - 6*(7 + 2x) = 7x + (-3)*5x + (-3)*2 + (-6)*7 + (-6)*2x
= 7x - 15x - 6 - 42 - 12x
= 7x - 15x - 12x - 6 -42 {Combine like terms}
= -20x - 48
The length and width of a rectangle are consecutive even integers. The perimeter is 92 meters. Find the length and width!
Answers
Answer:
w represents the width
w + 2 represents the length
2(w + w +2) = 76 formula for perimeter
w + w + 2 = 38 divide both sides by 2
2w + 2 = 38 combine like terms
2w = 36 subtract 2 from both sides
w = 18 divide both sides by 2
Which conditional probabilities are correct? check all that apply. p(d | f) = startfraction 6 over 34 endfraction p(e | d) = startfraction 7 over 25 endfraction p(d | e) = startfraction 7 over 25 endfraction p(f | e) = startfraction 8 over 18 endfraction p(e | f) = startfraction 13 over 21 endfraction
Answers
The conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
How to determine the true conditional probabilities ?The conditional probability P(A|B) is calculated using:
P(A | B) = P(A and B)/P(B)
Using the above formula and the data in the complete question (see attachment), we have the following computations:
P(D | F) = 6/34
P(E | D) = 7/25
P(D | E) = 7/18
P(F | E) = 8/18
P(E | F) = 8/34
By comparing the above computations with the options, the conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
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Answer:
A, B, D
Step-by-step explanation:
yw :)
If f(x) = 3x+2, find f(f¹(14))
Answers
Answer:
f(f¹(14)) = 134
Step-by-step explanation:
Given :
f(x) = 3x + 2Find the value of f(14) :
f(14) = 3(14) + 2f(14) = 42 + 2f(14) = 44Therefore, f(f¹(14)) = f(44).
Solving :
f(44) = 3(44) + 2f(44) = 132 + 2f(f¹(14)) = 134the diagram represents a rectangular garden of length 14 m and width 10 m
The flower bed is a triangle and the vegetable patch is a trapezium
the rest of the garden is lawn
Answers
Answer:
The area of the lawn is 68 [tex]m^2[/tex].
Step-by-step explanation:
Area of lawn = Area of garden - (Area of triangle + Area of trapezium)
Area of garden = length x width
= 14 x 10
= 140 [tex]m^2[/tex]
Area of triangle = [tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] x 3 x 8
= 12 [tex]m^2[/tex]
Area of trapezium = [tex]\frac{1}{2}[/tex] (a + b) h
= [tex]\frac{1}{2}[/tex](5 + 7) 10
= 60 [tex]m^2[/tex]
So that;
Area of lawn = 140 - (12 + 60)
= 140 - 72
= 68
The area of the lawn is 68 [tex]m^2[/tex].
how do I solve this?
Answers
What is the full number (all 0's and what not) of 4.385e+30
Answers
Answer:
4 385 000 000 000 000 000 000 000 000 000.
Step-by-step explanation:
Wellllll.....e +30 means 10^30
3.2 × 10^7
write in expanded form
Answers
Answer:
32000000
Step-by-step explanation:
3.2 x 10 = 32
you will have 10^6 left
32 x 10^6 = 32000000
just add 6 zeroes
Answer:
32, 000, 000.
Step-by-step explanation:
3.2 x 10^7 <======= move the decimal 7 places to the right
32,000,000.
Please help me on this question I’m very confused I will give you brainless??
Answers
To solve this problem, we need to use the theorem which states that the sum of angles in a triangle is equal to 180 degrees. The value of m<FED is equal to 120 degrees. From the diagram given, m<CBD is complimentary with m<BED
Sum of Angles in a TriangleThe value of m<FED can be calculated by summing the entire entity and equating to 180 degrees.
Data;
m<FED = (16x - 8)m<EFD = 35m<EDF = 2x + 9[tex]35+(16x-8)+(2x+9) = 180[/tex]
Reason: The sum of angles in a triangle is equal to 180 degrees.
But we would need to solve for the value of x.
[tex]35+(16x-8)+(2x+9) = 180\\35 + 16x - 8 + 2x + 9 = 180\\36+ 18x = 180\\180 - 36 = 18x\\18x = 144\\x = \frac{144}{18} \\x = 8[/tex]
Let's substitute the value of x into m<FED
[tex]m < FED = 16x - 8\\x = 8\\m < FED = 16(8) - 8 \\m < FED = 128 - 8\\m < FED = 120^0[/tex]
The value of m<FED is equal to 120 degrees.
From the diagram given, m<CBD is complimentary with m<BED
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