Step-by-step explanation:
For a log,
\( log_{b}(x) = y\)
To write it in exponent form,
\(b {}^{y} = x\)
For example,
\( log_{4}(64) = 3\)
In exponential form is
\(4 {}^{3} = 64\)
While
\(5 {}^{2} = 25\)
In log form is
\( log_{5}(25) = 2\)
Work out the equation of the line, which has a gradient of 3 and passes through the point (-1,3)
Answer:
Step-by-step explanation:
The equation of the line can be found using the point-slope form:
y - y1 = m (x - x1)
where m is the gradient, (x1, y1) is a point on the line.
For the given information:
m = 3, x1 = -1, y1 = 3
Plugging in the values into the point-slope form:
y - 3 = 3 (x - (-1))
Simplifying the equation:
y = 3x + 6
So, the equation of the line is: y = 3x + 6
I don't need lengthy details I just want the answer
Answer:
Sue rode 1885 miles total
Step-by-step explanation:
There are 31 days in March, 30 in April, and 30 in May.
31 * 12 + 30 * 12 + 30 * 12 = 1092
There are 30 days in June and 31 in august.
30 * 13 + 31 * 13 = 793
Now we find the total:
1092 + 793 = 1885
Plz help an show work thank u
2. 4g - 4 = 28
(add 4 on both sides) 4g = 32
(divide by 4 on both sides) g = 8
4. 0.5y - 1.1 = 4.9
(add 1.1 on both sides) 0.5y = 6
(subtract 0.5 on both sides) y = 5.5
6. 6t - 1/6 = 9
(add 1/6 on both sides) 6t = 9 1/6
(divide by 6 on both sides) t = 1.52777778
What is a biome?
A
B
C
What’s the correct answer answer asap for brainlist
Option A
Step-by-step explanation:A large naturally occurring community of flora and fauna occupying a major habitat, e.g. forest or tundra. A biome is a large area characterized by its vegetation, soil, climate, and wildlife.
A certain form of cancer is known to be found in women over 60 with probability of 0.07. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative (i.e. the test incorrectly gives negative result when the woman actually has the cancer) and 5% of the time the test gives false positive (i.e. incorrectly gives a positive result when the woman actually does not have the cancer). What is the probability that a randomly selected woman over 60 will test positive?
Answer:
Throughout the segment below, the definition including its particular question is mentioned.
Step-by-step explanation:
The probability of developing cancer
= 0.07
The probability of someone not getting cancer
= 1 - 0.07
= 0.93
Provided that if women have cancer, the risk of someone not testing positive is:
= 0.10
Therefore, if a female requires cancer, the risk of testing positive
= 1 - 0.10
= 0.90
The Probability of positive test
= 0.055 (whenever a woman does not have cancer)
Therefore, whenever a woman does not have cancer, the risk of not testing positive will be:
= 1 - 0.05
= 0.955
Now,
By using the law of conditional probability, we get
⇒ \(P(\frac{B}{A} ) = \frac{P(A \ and \ B)}{P(A)}\)
⇒ \(P (A \ and \ B) = P(A)\times P(B)\)
⇒ P (having cancer as well as positive tests) = P(having cancer) × P(Effective results, because she has cancer)
⇒ \(0.07\times 0.90\)
⇒ \(0.063\)
Correspondingly,
P (not getting cancer and testing effective or positive)
= \(0.93\times 0.05\)
= \(0.04655\)
P (with a good test result)
= \(0.063 + 0.0465\)
= \(0.1095\)
The volume of a sphere depends on its radius, so the volume is a function of the radius. If this function is called V(r), use the formula below to compute V(4), the volume of a sphere with a radius of 4 units.
Answer:
the volume of a sphere with a radius of 4 units.
=4/3πr³=4/3×π×64 is your answer
answer this question please
Step-by-step explanation:
this is just a warm-up. almost everything is already there. you only need to put the numbers in.
so, what is unclear ?
please, tell me, so that I can help better.
the radius is always half of the diameter. or the diameter is twice the radius.
in our case : 12/2 = 6 cm.
the height is plainly written in the graph : 9 cm
Vcylinder = base area × height = pi×r² × height =
= 3.14 × 6² × 9 = 3.14×36×9 = 1,017.36 cm³
Vcone = 1/3 × Vcylinder = 1/3 × 1,017.36 = 339.12 cm³
A hiking trail is shown as 14 cm on a map.
The scale is 1 : 150000
How far in km is it in real life?
Answer:
21km
Step-by-step explanation:
1km=100000cm
14x150000=2100000cm=21km
The distance in real life in kilometers by the given scale factor will be 21 kilometers.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
As per the given,
Scale factor = 1 : 150000
It means 1 cm will convert to 150000 cm.
In real life = 14 x 150000 = 2100000 cm
2100000 cm = 21000 m = 21 kilometer
Hence "The distance in real life in kilometers by the given scale factor will be 21 kilometers".
To learn more about scale factors,
brainly.com/question/22312172
#SPJ6
Stella is using grid paper to make shapes. Her first shape has an area of 14 square units. Her second shape has an area of 28 square units. Her third shape has an area of 42 square units. If this pattern continues what will be the area of her fourth shape
Answer:
56
Step-by-step explanation:
The pattern is an arithmetic sequence:
by the first three terms, the common difference is:
28-14=42-28=14
So the next pattern would be:
14+42=56
By the equation x = a + d ( n - 1 )
Substituting when n=1, x=14 and when n=2 x=28
a = 14 and d = 14
x = 14 + 14 ( n - 1 )
substituting n = 4
x = 14 + 14 ( 4 - 1 )
x = 56
28÷14=42-28=14+42=56
CAN SOMEONE HELP WITH THIS QUESTION?✨
As a result, when the camera and the rocket are 4255 feet apart, the rate trigonometry of change in the angle of elevation after launch is roughly -0.15807 radians/foot.
what is trigonometry?Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.
Where is the camera's angle of elevation and c is the rocket's height above ground level.
We may express the angle of elevation using the given formula as:
r θ = tan⁻¹(c/2000)
c2 + x2 = d2, where d = 4255 ft 2c(dc/dx) + 2x = 0, and dc/dx = -x/c.
When we multiply c by 2000 tan() and x by (d2 - 20002) (since x is the horizontal distance between the camera and the rocket), we get: dc/dx = -(d2 - 20002) / (2000 tan())
tan1(0.02d/2000) = tan1(d/100000)
dc/dx = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -0.005(d2 - 20002) / d
dc/dx = -0.005(42552 - 20002) / 4255 -0.15807 radians per foot
As a result, when the camera and the rocket are 4255 feet apart, the rate of change in the angle of elevation after launch is roughly -0.15807 radians/foot.
To know more about trigonometry visit:
https://brainly.com/question/29002217
#SPJ1
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = −7 and x = 5 and passes through the point (0, −2).
The formula of the parabola is y = 2/35(x + 7)(x - 5)
How to determine the formula of the parabola?The parameters in the question are given as
Horizontal intercepts (roots) at x = −7 and x = 5 Passes through the point (0, −2).These parameters can be represented as
x₁ = -7 and x₂ = 5
(x, y) = (0, -2)
The quadratic function can be represented as
y = a(x - x₁)(x - x₂)
Substitute the known values in the above equation So, we have the following equation
y = a(x + 7)(x - 5)
At (x, y) = (0, -2), we have
-2 = a(0 + 7)(0 - 5)
Evaluate
a = -2/-35
Divide
a = 2/35
So, we have
y = 2/35(x + 7)(x - 5)
Hence, the equation is y = 2/35(x + 7)(x - 5)
Read more about parabola at
https://brainly.com/question/1480401
#SPJ1
A grocery store clerk can scan 1 product every 1/2 of a second. At what rate can she scan products?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
What is the slope of the line on the graph?
Enter your answer in the box.
9514 1404 393
Answer:
-2
Step-by-step explanation:
The rise between adjacent points (left to right) is -6, while the run is 3. Then the slope is ...
m = rise/run = -6/3 = -2
The slope of the line is -2.
What is the equivalent equation solved for h?
Answer:
\(h=\frac{P}{mg}\)
Step-by-step explanation:
If you divide both sides of this equation by mg, you are left with \(h=\frac{P}{mg}\), which is the equivalent solution solved for h. Hope this helps!
Answer:
it's B
Step-by-step explanation:
C.
D.
83-74-75-8
E
A motorist drives 150km from Abuja to Jo's in 1
hour 15 minutes, his average speed in
Answer:
the answer to this question is 120km/hr
Answer:
120 km per hour
Step-by-step explanation:
150 / 1.25 = 120 km per hour
Tell whether each equation is true, false, or open. Explain.
2.) 5x+7 = 17
1.) 85+ (-10) = 95
3.) -8(-2) - 7 = 14 – 5
Answer:
1.) 85+ (-10) = 95 is false.
2.) 5x+7 = 17 is false.
3.) -8(-2) - 7 = 14 – 5 is false.
Step-by-step explanation:
1. is false because since 85 ≠ 95, then 85 + ( - 10) = 95 is false.
2. is false because since 12 ≠ 17, then 5x + 7 = 17 is false.
3. is false because since -15 ≠ 14, then -8( - 2) - 7 = 14–5 is false.
Solve this inequality, and write your answer in interval notation.
|x|>−5
The solution set for the inequality |x|>−5 is:(-∞, ∞)
How to solve the inequality?Here we have an inequality with an absolute value: |x|>−5
Now, this is particularly trivial.
Remember that the absolute value is always zero or positive, this means that for all values of x, the absolute value of x will be larger than any negative number (particularly -5).
So the solution set is the set of all real numbers, written in interval notation this would be:(-∞, ∞)
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
16) Solve for side AB.
AB-
Round your answer to the nearest hundredth.
A) 5.45
B) 6.45
C) 7.45
Answer:
AB= 7.45
Anwer C)
Step-by-step explanation:
Cos (angle) = Nearest side / Huypothenuse
Cos(20) = 7 / AB
Cos(20) * AB = (7 /AB) * AB
Cos (20) * AB = 7
(Cos(20) *AB) / Cos(20) = 7 / Cos(20)
AB = 7 / cos(20)
AB= 7.45
I cannot solve the equation.
√(7d+1)-4=11
Answer:
I believe the answer is d = 32
Step-by-step explanation:
You should isolate the radical, then raise each side of the equation to the power of its index.
9514 1404 393
Answer:
d = 32
Step-by-step explanation:
Add 4, then square, and solve the resulting linear equation.
√(7d +1) = 15
7d +1 = 225 . . . . . . square both sides
7d = 224 . . . . . . . . subtract 1
d = 32 . . . . . . . . . . divide by 7
Which expression is equivalent to
Answer:
D
Step-by-step explanation:
x^2 - 7x + 12 + (x - 3)^2 Add (x - 3)^2 after it has been expanded.
x^2 - 7x + 12 + x^2 - 6x + 9 Combine like terms
2x^2 -7x - 6x + 21
2x^2 - 13x + 21 Factor
(2x - 7)(x - 3)
Which is exactly what D says.
I’m am really confused on this question
Answer:
2x^7
Step-by-step explanation:
add the exponents because they both are x
2x^4*x^3=2x^7
What is the exact volume of the cylinder?
O 187 in
O 367 in
O 547 in
O 637 in
My
Which expression is equivalent to √216x²7?
O 6x³
O 6x⁹
O 72x³
O 72x⁹
Answer:
The answer to this question is 72x3
here is an inequality: -3x > 18 list some values for x that would make this inequality true
Step-by-step explanation: First, we need to solve this inequality.
When you're asked to solve an inequality like -3x > 18, your goal should be the same as it was when solving equations, to get x by itself on one side.
In this problem since x is being multiplied by -3 on the left side of the inequality, to get x by itself, we divide both sides by -3 but here is the rule you have to watch out for when solving inequalities.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign. So this greater than in our original problem becomes less than in our second step.
On the left side, the -3's cancel and we're left with
x and on the right side, 18 divided by -3 is -6.
So we have x < -6.
Now, we are asked to state some solutions to the inequality.
The inequality x < -6 means that any number
less than -6 is a solution to the inequality.
For example, -7 is a solution because -7 is less than -6.
-8 is also a solution because -8 is less than -6.
Other possible solutions include -23, -98, -982, and so on.
Any number less than -6 will be a solution.
I need help on my math hw
Because the sum of the internal angles must be equal to 180°, we will see that x = 43.75
How to find the value of x?
Here we need to remember that the sum of the internal angles of a triangle always gives 180°, so we can write:
(x + 10)° + (3x - 5°) + x° = 180°
Now we need to solve this linear equation for x.
4x + 5= 180
4x = 180 - 5 = 175
x = 175/4 = 43.75
The value of x is 43.75
If you want to learn more about triangles, you can read:
https://brainly.com/question/2217700
If m < 8 = 106 and m < 3 = (6x-4) what is the value of x.
a. x = 11
b. x = 12
c. x = 13
d. x = 18
please help
Which set of values could be the side length of a 30 60 90 triangle? A. {5,5v3,10}
Therefore, the answer is A. {5, 5√3, 10}.
The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.
In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.
Let's check if the given set of values satisfies this ratio:
If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.
For such more question on lengths
https://brainly.com/question/28322552
#SPJ8
HELP NEEDED ASAP
2. Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid. [1mark]
b) State the following for the transformed function [2marks]
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
The five key points of the parent function are:
Domain: Set of all real numbersRange: Set of all real numbers from -1 to 1 (inclusive)No vertical asymptoteNo horizontal asymptoteMaximum: (π/2 + 2πn, 1)The five key points of the parent functionThe function is given as:
y = -2 sin[2(x - 45)] + 1
The above function is a sine function, and the parent function of a sine function is
y = sin(x)
The properties of the above function are:
Domain: Set of all real numbersRange: Set of all real numbers from -1 to 1 (inclusive)No vertical asymptoteNo horizontal asymptoteMaximum: (π/2 + 2πn, 1)The transformed functionThe transformed function is given as:
y = -2 sin[2(x - 45)] + 1
A sine function is represented as:
y = A sin[Bx + C] + D
Where:
A represents the amplitudePeriod = 2π/BC represents horizontal phase shiftUsing the above representations, we have:
Amplitude = -2Period = 2π/2 = πHorizontal phase shift, C = 2 * -45 = -90Equation of the axis, y = 1The graph of the functionSee attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1
Read more about sine functions at:
brainly.com/question/9565966
#SPJ1
Maria rides her bicycle a distance,d, of 40 meters. If her riding time,t, is 10 seconds, what is her rate of speed, r, in meters per second?
A. 1/400
B. 1/4
C. 4
B. 400
Answer: C
Step-by-step explanation:
i had this question and got t right with C
A pack of gum that comes with 35 pieces is $2.88 how much is one piece of gum? (unit price)
Answer:
0.08
Step-by-step explanation: