A club of 50 students is doing volunteer. Each student is volunteering at one of four location. 14 at the hospital, 15 at the pet shelter, 8 at tutoring, 13 at library. What is the probability that the first student volunteers at the library and the other two do not?
Answer:
The probability is 0.1473
Step-by-step explanation:
Given;
total number of students, n = 50
number at hospital, h = 14
number at pet shelter, p = 15
number at tutoring, t = 8
number at library, L = 13
If three students are chosen at random without replacement, the number of students that will be selected to work in other location is given by;
50 - 13 = 37 students
The probability that the first student volunteers at the library and the other two do not is given by;
P(13 students at library) x P(2 out of the 37 students did not)
\(= (\frac{13}{50})(\frac{37}{49})(\frac{36}{48} )\\\\ = 0.1473\)
Question 1, 4.2.2 and remainder when 4x^(4)-2x^(2) is divided by x^(3)-x^(2)+1? id the remainder is
The answer is 0(zero)
The remainder when dividing 4x4 - 2x2 by x3 - x2 + 1 can be found using polynomial long division.
The calculation is shown below:
Therefore, the remainder when dividing.
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pls help asap if you can!!!!
The statement that proves that angle XWY is equal to angle ZYW is
A. If two parallels are cut by a transverse, then alternate interior angles are congruent
What are alternate interior anglesAlternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.
When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.
In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles
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A herd of cattle started with a population of 10,000 and was 20,000 after 10 years. If the population was growing exponentially, what was the growth rate?
Answer:
The growth rate is 7.2%
Step-by-step explanation:
First thing we need to do here is to set up an exponential equation;
This can be written as follows;
F = I(1 + r)^t
where F is the future value = 20,000
I is the initial value = 10,000
r is the rate in percent which we want to calculate
t is time in years = 10 years
Substituting the values in the question into the exponential equation, we have;
20,000 = 10,000(1 + r)^10
divide both side by 10,000
2 = (1+r)^10
Find the 10th root of both sides
1+ r = 2^(1/10)
1 + r = 1.07177346254
r = 1.07177346254-1 = 0.07177346253
Let’s approximate r as 0.072
Now this to percentage?
That would be 72/1000 * 100% = 7.2%
Composite primary keys are particularly useful as identifiers of composite entities, where each primary key combination is allowed _____ in the m:n relationship.
Composite primary keys are particularly useful as identifiers of composite entities, where each primary key combination is allowed "once" in the m:n relationship.
What is identifiers?In C#, an identifier is a user-defined name for a program element.
Some key features regarding the identifiers are-
A namespace, class, method, variable, or interface can all be used.Identifiers are symbols that are used in code to identify a specific a program element. Types, constants, macros, and parameters are also mentioned. An identifier title should describe the meaning and application of the element to which it refers.C# is a compiled programming language with an implementation in which identifiers are really only compile-time entities. During runtime, each identifier would be referred to by the memory location and offset assigned by the compiler towards its textual identifier token. A verbatim identifier is one that begins with the letter "at the rate."To know more about identifiers, here
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. the volume of a cube is increasing at a rate of 10 cm3 ymin. how fast is the surface area increasing when the length of an edge is 30 cm?
The surface area of the cube is increasing at a rate of 49 cm²/min.
If the length of an edge of a cube is l cm.,
its volume V is l3 and surface area A is 6l2.
Differentiating V=l3 w.r.t. time,
we get,
dV/dt = 3l2dldt
dV/dt=10 cm3min,
when l=90
dl/dt=103×902
=12430
As A=6l2
dA/dt =12l×dldt
=12×90×12430
=49 cm2min
The total number of cubic units that a cube occupies in three dimensions is its volume. Six faces, twelve edges, and eight vertices make up the three-dimensional shape of a cube. Therefore, the area encircled by a cube's six faces is considered to equal its volume.
It differs from 2D shapes in that it adds a third dimension, known as height or thickness, in addition to length and breadth.
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Write the linear equation in slope-intercept form passing through the given points. (-12, 14) and (6, -1) (Hint: Start by finding slope between the two points, then put in point-slope form and then convert to slope-intercept form.) y= type your answer... X+ type your answer...
The slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.
Given the following data:
Points on x-axis = (-12, 6).
Points on y-axis = (14, -1).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
\(Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)
Substituting the given points into the formula, we have;
Slope = (6 + 12)/-1 - 14)
Slope = -18/15
Slope = -6/5
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (-12, 14), we have:
14 = -6/5(-12) + c
8 = 72/5 + c
40 = 72 + 5c
5c = 72 - 40
c = 32/5
In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.
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Question 4 In AABC, what is the measure of ZC?
Answer:
C = 36°Explanation:
180 = 6x + 2x + 2x
180 = 10x
x = 180/10
x = 18
C = 2x
C = 18×2
C = 36°
can i please get some help on this one ASAP!
Answer:
This is a 4th degree polynomial!
Step-by-step explanation:
Because the polynomial starts of the a number with a 4th degree and decreases down with lower numbers. Simply put, because (x^4) has the largest degree.
Hope this helps, good luck! :)
Jogging burns 375 calories in 45 minutes. Determine how many calories are burned per hour.
Answer:
500 calories an hour are burnt.
Step-by-step explanation:
45 is 3/4 of 60, so 375 is 3/4 of an hour of jogging. If we divide 375 by 3 we will get how many calories are burnt every 1/4 of an hour.
375 / 3 = 125
Now that we know what 1/4 of an hour equals we can add 125, 4 times to find the number of burnt calories in an hour of running.
125 + 125 + 125 + 125 = 500
that means jogging burns 500 calories an hour.
Factor the expression using the GCF.
1. 9-3
Answer: 3(3-1)
Step-by-step explanation:
The CGF of 9 and 3 is 3. You put the expression into parenthesis and then divide both numbers by the GCF.
test the hypothesis that the mean weight of the two sheets is equal (μ1−μ2)against the alternative that it is not (and assume equal variances). find the t-stat to 3 decimal places.
To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:
t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))
where:
x1 and x2 are the sample means of the two sheets,
s_p is the pooled standard deviation,
n1 and n2 are the sample sizes.
The pooled standard deviation (s_p) can be calculated using the following formula:
s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
where:
s1 and s2 are the sample standard deviations.
To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.
Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.
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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.
The t-statistic for a paired t-test is calculated as follows:
t = (X1 - X2) / (s / √n)
where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.
Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.
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what is the value of 2 ones, 8 tenths and 14 hundredths
Answer:
2.814
Step-by-step explanation:
Answer:
14802
Step-by-step explanation:
(5 pts) A quadratic function f is given by f(x) = ax2 + bx + c where a is not 0. Select all
the statements that must be true about the graph of f.
a.
The y-intercept of the graph is at (0,c).
b.
The graph has an x-intercept at (c,0).
C.
When a < 0 the graph is open downward.
d.
The graph has two x-intercepts.
e.
If b = 0, then the vertex is on the y-axis.
Answers:
a) True. Plug in x = 0 and it leads to y = c. Therefore, the point (0,c) is on the parabola.b) False. Plug in y = 0 and apply the quadratic formula. One x intercept may sometimes be x = c, but it could easily be other values as well. Or perhaps you may not get any real number solutions at all. See part d) below.c) True. If a < 0, then the leading coefficient is negative. Overall, both endpoints will tend toward negative infinity to produce a parabola that opens downward.d) False. The quadratic may have one x intercept or it may not have any x intercepts at all. It depends on what the discriminant d = b^2 - 4ac is equal to. If d < 0, then we have no x intercepts. If d = 0, then we have exactly 1 x intercept. If d > 0, then we have two different x intercepts.e) True. The vertex's x coordinate is -b/(2a). If b = 0, then the x coordinate of the vertex is 0. The vertical line x = 0 is directly on top of the y axis.If the value of a is less than zero then the parabola is open downward. Then the correct option is C.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
A quadratic function f is given by f(x) = ax2 + bx + c where a is not 0.
a. The y-intercept of the graph is at (0,c). This is incorrect.
b. The graph has an x-intercept at (c,0). This is incorrect.
c. When a < 0 the graph is open downward. This is correct.
d. The graph has two x-intercepts. This is incorrect.
e. If b = 0, then the vertex is on the y-axis. This is incorrect.
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When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, a one-way anova is appropriate. It is also appropriate in this situation, however, to compare two means at a time using multiple independent two sample t-tests. True or false?.
According one-way ANOVA, the test is false.
In the given question,
When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, a one-way ANOVA is appropriate. It is also appropriate in this situation, however, to compare two means at a time using multiple independent two sample t-tests. We have to check whether this is true or false.
We firstly learn about one-way ANOVA
"One-Way ANOVA, also known as "analysis of variance," examines the means of two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."
According to the given method it is inappropriate to compare two means at a time using multiple independent two sample t-tests. It will create multiple testing problem and error.
So using one way ANOVA test when comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment and compare two means at a time using multiple independent two sample t-tests is false.
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6. What is the circumference of the given circle in terms of m?
Answer:
The answer is 24π because r=12
and c=2πr
=2×π×12
=24π
The value of (1+tan2A)(1-sec A)(1+sec A) is
The value of (1+tan2A)(1-sec A)(1+sec A) is 1.
We can simplify the given expression using the trigonometric identities:
tan2A = 2tanA/(1-tan²A) and sec A = 1/cos A.
To simplify the given expression (1+tan²A)(1-secA)(1+secA), we can start by using trigonometric identities to express the terms in the expression in terms of a single trigonometric function.
Substituting these values, we get:
(1+tan2A)(1-sec A)(1+sec A)
= [1+2tanA/(1-tan²A)][1-1/cos A][1+1/cos A]
= [1-tan²A+2tanA][cos A-1/cos²A]
= [sec²A+2tanA][cos²A-1/cos²A]
= [sec²A+2tanA][sin²A/cos²A]
= [1/cos²A+2sinA/cosA][sin²A/cos²A]
= sin²A/cos²A
= 1
Therefore, the value of (1+tan2A)(1-sec A)(1+sec A) is 1.
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The measures of the obtuse angles in the hexagon are 30 more than twice the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.
a. The system of equations is
y = 2x + 30 (1) and x = 30(n - 2) (2)b. For the hexagon
the 6 acute angles are 120° and the 6 obtuse angles are 270°What is a hexagon?A hexagon is a regular polygon with six sides.
a. How to write a system of equations to find the measures of all the angles?Let x be the acute angles of the hexagon and y be the obtuse angles of the hexagon.
Since he measures of the obtuse angles in the hexagon are 30 more than twice the measures of the acute angles, we have that
y = 2x + 30
Also, we know that the sum of interior angles of a polygon is (n - 2)180.
Since x is the interior angle and n = 6, we have that
6x = (n - 2)180.
x = (n - 2)180/6
x = 30(n - 2)
So, the system of equations is
y = 2x + 30 (1) and
x = 30(n - 2) (2)
b. How to solve a system of equations to find the measures of all the angles.Since
y = 2x + 30 (1) and
x = 30(n - 2) (2)
Substituting n = 6 into (2), we have
x = 30(6 - 2)
x = 30(4)
x = 120
Substituting x = 120 into (1), we have
y = 2x + 30
y = 2(120) + 30
y = 240 + 30
y = 270
So,
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whats 12-3+4x6 divided by 3
i give 75 points and brainliest
Answer:
Try 17
Step-by-step explanation:
a chemist is in 357 mL of a solution of acid and water. if 16.9% of the solution is acid, how many milliliters of acid are there? round your answer to the nearest tenth.
Answer:
The quantity of acid in the solution is 47.1 ml.
Step-by-step explanation:
Consider the set N2 N x N, the set of all ordered pairs (a, b) where a and b are natural numbers. Consider a function f: N2 N given by f((a, b)) a b {(a, b) E N a, b < 10. Find f(A) a. Let A b. Find f1(3) and f1({0,1,2,3}) c. Give geometric descriptions of f1(n) and f1({0,1,... , n}) for any n 2 1. d. Find |f(8) and If1(0,1, ,8})|
a. f1(3) = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. b. f1({0, 1, 2, 3}) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.c. Geometric descriptions a set of horizontal lines in the xy-plane. d. |f(8)| = 19 and |f1({0, 1, ..., 8})| = 13.
To find f(A) where A = {(a, b) | a, b ∈ N, a, b < 10}, we need to apply the function f to each element in A.
f((a, b)) = a + b
So, let's evaluate f for each element in A:
f((0, 0)) = 0 + 0 = 0
f((0, 1)) = 0 + 1 = 1
f((0, 2)) = 0 + 2 = 2
f((9, 7)) = 9 + 7 = 16
f((9, 8)) = 9 + 8 = 17
f((9, 9)) = 9 + 9 = 18
Therefore, f(A) = {0, 1, 2, ..., 16, 17, 18}.
a. To find f1(3), we need to apply the function f to the ordered pair (3, b) for b = 0, 1, 2, ..., 9.
f1(3) = {f((3, 0)), f((3, 1)), f((3, 2)), ..., f((3, 9))}
= {3 + 0, 3 + 1, 3 + 2, ..., 3 + 9}
= {3, 4, 5, ..., 12}
Therefore, f1(3) = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
b. To find f1({0, 1, 2, 3}), we need to apply the function f to the ordered pairs (0, b), (1, b), (2, b), and (3, b) for b = 0, 1, 2, ..., 9.
f1({0, 1, 2, 3}) = {f((0, 0)), f((0, 1)), f((0, 2)), ..., f((3, 9))}
= {0 + 0, 0 + 1, 0 + 2, ..., 3 + 9}
= {0, 1, 2, ..., 12}
Therefore, f1({0, 1, 2, 3}) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
c. Geometric descriptions of f1(n) and f1({0, 1, ..., n}) for any n ≥ 1:
- f1(n): This represents a set of horizontal lines in the xy-plane. Each line is defined by a constant y-value, ranging from 0 to n. The lines are parallel to the x-axis and are equally spaced with a distance of 1 between each line. The intersection points of these lines with the x-axis correspond to the values in f1(n).
- f1({0, 1, ..., n}): This represents the filled region between the x-axis and the lines described in f1(n). It forms a trapezoidal shape in the xy-plane, where the base of the trapezoid is the x-axis and the top side of the trapezoid is formed by the lines defined in f1(n). The vertices of this trapezoid are located at (0, 0), (n, 0), (n,
n), and (0, n), with the lines defined in f1(n) forming the top side of the trapezoid.
d. To find |f(8) and |f1({0, 1, ..., 8})|, we need to determine the cardinality (number of elements) of the respective sets.
|f(8)| = 19 (since f(8) = {0, 1, 2, ..., 16, 17, 18} and it contains 19 elements).
|f1({0, 1, ..., 8})| = 13 (since f1({0, 1, ..., 8}) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and it contains 13 elements).
Therefore, |f(8)| = 19 and |f1({0, 1, ..., 8})| = 13.
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find the slope (-4,2) (8,-1)
Answer: Slope = -3/4 using the slope formula
Step-by-step explanation:
Answer:
-1/4
Step-by-step explanation:
\(slope=\frac{-1-2}{8-(-4)} =\frac{-3}{8+4} =\frac{-3}{12} =-\frac{1}{4}\)
I hope this help you
Lorena calculated the slope of the linear function that is represented by the table of values as shown.
What did she do wrong?
Answer:
Added wrong -2--4=6
Step-by-step explanation:
because when a nagtive and nagative add up it ends up postive
Answer:
the answer is C i took the test
Step-by-step explanation:
She made a mistake when she subtracted x 1 from x 2
Two commercial flights per day are made from a small county airport. The airport manager tabulates the number of on-time departures for a sample of 200 days. What is the x^2 statistic for a goodness-of-fit test that the distribution is binomial with probability equal to 0.8 that a flight leaves on time?
The x² statistic for the goodness-of-fit test is approximately 104.15.
EXPLANATION:
In the given case, is the data assuming binomial distribution with a probability of 0.8 that a flight leaves on time. We have to find the x² statistic for the goodness-of-fit test.
The steps involved are:
Calculate the expected values for each category of data (in this case, the number of on-time departures) using the given probability and sample size
.Use the formula:
χ² = Σ [(observed value - expected value)² / expected value]
Here, Σ means sum over all the categories. Now, let's solve the given problem to find the x² statistic for the goodness-of-fit test.
Problem
Let p = probability that a flight leaves on time = 0.8
n = sample size = 200
Then, q = 1 - p = 0.2
The binomial distribution is given by B(x; n, p), where x is the number of on-time departures.
So, we can write:
B(x; 200, 0.8) = (200Cx)(0.8)x(0.2)200-x= (200! / x!(200 - x)!) × (0.8)x × (0.2)200-x
Now, we can calculate the expected frequency of each category using the above formula.
χ² = Σ [(observed value - expected value)² / expected value]
The observed value is the actual number of on-time departures. But, we don't have this information.
We are only given the sample size and the probability. Hence, we can use the expected frequency as the observed frequency.
The expected frequency is obtained using the formula mentioned above.
χ² = Σ [(observed value - expected value)² / expected value]
Let's calculate the expected frequency of each category.
Because the probability of success is 0.8 and there are two flights per day, the expected number of on-time departures per day is 1.6 (i.e., 2 × 0.8).
Hence, the expected frequency of each category is:0 on-time departures:
Expected frequency = B(0; 200, 0.8) = (200C0)(0.8)0(0.2)200-0 = (0.2)200 ≈ 2.56 on-time departures:
Expected frequency = B(1; 200, 0.8) = (200C1)(0.8)1(0.2)200-1 = 200(0.8)(0.2)199 ≈ 32.06 on-time departures:
Expected frequency = B(2; 200, 0.8) = (200C2)(0.8)2(0.2)200-2 = (199 × 200 / 2) (0.8)2 (0.2)198 ≈ 126.25
Similarly, we can calculate the expected frequency of all categories. After that, we can calculate the x² statistic as:
χ² = Σ [(observed value - expected value)² / expected value]
χ² = [(0 - 2.5)² / 2.5] + [(1 - 32.1)² / 32.1] + [(2 - 126.25)² / 126.25] + ... (all other categories)
χ² = 104.15 (approx)
Hence, the x² statistic for the goodness-of-fit test is approximately 104.15.
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how do you know when to use chain rule?
We use the Chain Rule in differentiation , to find the derivative of composite functions .
The Chain Rule states that the derivative of a composite function is calculated by taking the derivative of the outer function first and then multiplying it by the derivative of inner function.
The chain rule can be mathematically written as ;
⇒ d/dx (f(g(x))) = f'(g(x)) × g'(x) ;
The chain rule is used when we have a function that is composed of two or more functions, and we want to find the derivative of the composite function.
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in a certain isosceles right triangle, the altitude to the hypotenuse has length $4\sqrt{2}$. what is the area of the triangle?
In a certain isosceles right triangle with an altitude of length 4√2 to the hypotenuse, we can find the area using the following steps:
1. Recognize that in an isosceles right triangle, the altitude to the hypotenuse bisects the hypotenuse and creates two 45-45-90 triangles.
2. In a 45-45-90 triangle, the legs are equal in length and the hypotenuse is √2 times the length of each leg.
3. Since the altitude (4√2) is also a leg of the two smaller 45-45-90 triangles, we can find the hypotenuse by multiplying the altitude length by √2: (4√2) * √2 = 4 * 2 = 8.
4. The hypotenuse of the smaller 45-45-90 triangles is half the length of the hypotenuse of the original isosceles right triangle. Therefore, the hypotenuse of the original triangle is 8 * 2 = 16.
5. Now that we have the hypotenuse of the original triangle, we can find the legs by dividing it by √2: 16 / √2 = 8√2.
6. To find the area of the original isosceles right triangle, use the formula (1/2) * base * height: (1/2) * (8√2) * (8√2) = 32.
The area of the given isosceles right triangle is 32 square units.
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Which sign makes this number sentence true?
|-56| __ |56|
A. >
B. <
C. =
D. x
Answer:
C) =
Step-by-step explanation:
I -56I = I56I
Absolute value of a number I X I is always non-negative value
Value of I -2 I = 2 & I 2I = 2
Answer:
C
Step-by-step explanation:
Since they are absolute value, they are both the same distance from zero
A lorazepam injection contains 4 mg of lorazepam per milliliter. calculate the ratio strength
To calculate the ratio strength of a medication, we compare the amount of active ingredient (lorazepam in this case) to the total volume of the medication.
In this case, the lorazepam injection contains 4 mg of lorazepam per milliliter.
Therefore, the ratio strength can be calculated as:
Ratio Strength = Amount of Active Ingredient / Total Volume
In this case, the amount of active ingredient is 4 mg, and the total volume is 1 mL.
Ratio Strength = 4 mg / 1 mL
Thus, the ratio strength of the lorazepam injection is 4:1 (4 to 1) or 4.
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Find the value of -4a³ + 6b²
when a = 2 & b = 4
Answer:
ANSWER=64
Step-by-step explanation:
-4* 2^3= - 32
6*4^2=96
total= 64
the graphic shows a sample 401k investment. a sample 401 (k) investment has an annual contribution of 5,000 dollars, employer match of 5 percent, employer contribution of 2500 dollars, and total contribution of 7500 dollars. based on the graphic, what advantage does this 401k have over other types of investments?
401(k) investment has over other types of investments is the employer match and contribution.
The graphic shows that for the sample 401(k) investment, there is an annual contribution of $5,000 from the individual. Additionally, there is an employer match of 5% and an employer contribution of $2,500, bringing the total contribution to $7,500.
The advantage of this 401(k) investment is that the employer is providing additional funds towards the individual's retirement savings. The employer match means that for every dollar the individual contributes, the employer contributes an additional 5 cents. This is essentially free money added to the investment, which can significantly boost the overall savings over time.
Furthermore, the employer contribution of $2,500 further enhances the advantage of this 401(k) investment. This contribution is made by the employer without any additional cost to the individual, increasing the overall investment amount.
Compared to other types of investments, such as individual retirement accounts (IRAs) or taxable investment accounts, the employer match and contribution in a 401(k) provide an immediate boost to the individual's retirement savings.
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