Answer:
a) Yes.
b) Yes.
Step-by-step explanation:
Meredith and Hillary both want coffe, but they don't know if the other two people do, therefore they can't know if everyone want coffee. If they didn't want coffee, their answer would have been just "no".
Aly knows that she doesn't want coffee, therefore she knows that not everyone wants coffee.
Hillary and Meredith said 'I don't know' which implies they don't know if everyone wants coffee because they themselves do not want it. Aly confirmed that not everyone wants coffee. Therefore, neither Hillary nor Meredith got a coffee.
We have a logical puzzle where Hillary, Meredith, and Aly are deciding whether they want coffee. The key to solving this puzzle is understanding the implications of their statements to the waiter's question: "Does everyone want coffee?"
Hillary says, "I don't know." This means Hillary cannot be sure that everyone wants coffee, so there are two possibilities: either she does not want coffee or she doesn't know the preferences of the others. Meredith also responds with "I don't know," implying the same possibilities for her.
Finally, Aly states, "Not everyone wants coffee." This is the definitive answer that tells us at least one person does not want coffee. Since Aly knows for sure that not everyone wants coffee, it implies that either she does not want coffee herself or knows of someone else who doesn’t. Given that Hillary and Meredith both said they did not know, they could not have communicated their preference to Aly.
Therefore:
Hillary did not get a coffee, because if she did want coffee, she would have known that at least she herself wants coffee and would not have said, "I don't know."Meredith did not get a coffee either for the same reason as Hillary.Let f be continuous on [0, a] and differentiable on (0, a), Prove that if f(a)=0 then there is at least one value of x in (0, a), such that f(x)= -xf'(x).(5marks) (%4h) 4
Answer:
See picture attached
Step-by-step explanation:
246, 299, 360, 404, 379, 199, 279, 749, 794, 849, 914
Compute the mean, median, and mode of these prices.
Find the first and third quartiles of the prices.
Answer:
Mean = 497.5
Median = 379.0
First Quartile = 289
Third Quartile = 771.5
Step-by-step explanation:
Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations.
⇒ [tex]Mean=\frac{246+ 299+ 360+ 404+ 379+ 199+ 279+ 749+ 794+ 849+ 914}{11}[/tex]
⇒ Mean = 497.5
Median is the middle observation of given data. It can be found by following steps:
Arranging data in ascending or descending order.
Taking the average of middle two value if the total number of observation is even, and this average is our median.
or, if we odd number of observation then the most middle value is our median.
Here, number of observation is 11.
So the middle value is (11+1)÷2 = 6th term
⇒ Median = 379
The mode is the observation which has a high number of repetitions (frequency).
Here frequency of all observation is same. So, it is multi- modal data.
First Quartile is the middle value between Minimum value and Median of data after arranging data in ascending order.
First Quartile (Q₁) = 289
The third Quartile is the middle value between Median and Maximum Value of data after arranging data in ascending order.
Third Quartile (Q₃) = 771.5
The Cutty Sark is a famous clipper ship (look it up)! A Cutty Sark model kit advertises a scale ratio of 1: 78, a length of 45 inches, and a height of 26 inches.
A. How long was the Cutty Sark, according to this model kit?
B. How tall was the Cutty Sark, according to this model kit?
Answer: If the ratio is 1:78, a) the Cutty Sark is 3510 inches long or 292.5 ft; b) the Cutty Sark is 2028 inches tall or 169 ft according to this model
Step-by-step explanation: The ratio indicates that for every inch of the model, it corresponds to 78 inches of the actual size. If the length is 45 inches for the model, it would be an equivalent of 45*78 of the actual size = 3510 inches. The same can be applied to the height. Multiplying 26 x 78, the actual size should have a height of 2028 inches.
Hey guys, I was having a hard time with the following question and was wondering if someone can clear it up for me.
Solve sinθ+1 = cos2θ on the interval 0 ≤ θ < 2π
Two sides of a triangle are 4 m and 5 m in length. Express the area A of the triangle in terms of the angle Q between these two sides.
Answer:
The area of the triangle, as a function of the angle between the two given sides, is: [tex]A(Q) = 10sin(Q)\ m^{2}[/tex]
Step-by-step explanation:
We know that the area of a triangle is given by the formula A = b*h/2, where b stands for the base and h for the height.
In our problem, we can choose anyone of them as the base. Let us choose, for example, b = 5 m. Now that we know the value of the base, we can use the value of the other side (4 m) and the angle between these two sides (Q) to calculate the height:
[tex]h = (4 m)sin(Q)[/tex]
Therefore, the are of the triangle, as a function of the angle between these two sides is:
[tex]A(Q) = b*h/2 =5*4*sin(Q)/2\ m^{2} = 10sin(Q)\ m^{2}[/tex]
A loan of $19,221 was repaid at the end of 17 months. What size repayment check (principal and interest) was written, if a 9.7% annual rate of interest was charged? The amount of the repayment check was $ 45447.53). (Round to two decimal places.)
Answer:
The amount of the repayment check was $21862.29.
Step-by-step explanation:
Principal P = $19221
Rate r = 9.7% = 0.097
Time t = 17 months = [tex]17/12= 1.41667[/tex] years
[tex]I= p\times r\times t[/tex]
[tex]I= 19221\times0.097\times1.41667[/tex] = $2641.29
The loan repayment is the original principal plus the interest.
= [tex]19221+2641.29=21862.29[/tex] dollars
The amount of the repayment check was $21862.29.
Pierre Hugo is handling the estate of a prominent businesswoman. The will states that the surviving spouse is to receive one half of the estate and the remaining one half
of the estate will be divided equally among four surviving children. What fraction of the estate does each child receive?
Answer:
Each child will receive 0.125 (or 12.5%) of the estate.
Step-by-step explanation:
If the surviving spouse gets one half of the estate, the other half have to be divided among the four surviving children.
So its 0,5 divided among the 4 surviving children. That is 0.125 or 12.5% of the estate.
Each child will receive 0.125 of the estate.
Answer:
receive 0.125 (or 12.5%) of the estate.
Step-by-step explanation:
Suppose U is a nonempty subset of the vector space V over eld F. Prove that U is a
subspace if and only if cv + w 2 U for any c 2 F and any v;w 2 U
Answer:
The additive identity of [tex]V[/tex], denoted here by [tex]0_{V}[/tex], must be an element of [tex]U[/tex]. With this in mind and the provided properties you can prove it as follows.
Step-by-step explanation:
In order to a set be a vector space it is required that the set has two operations, the sum and scalar multiplication, and the following properties are also required:
Conmutativity. AssociativityAdditive IdentityInverse additiveMultiplicative identityDistributive properties.Now, if you have that [tex]V[/tex] is a vector space over a field [tex]\mathbb{K}[/tex] and [tex]U\subset V[/tex] is a subset that contains the additive identity [tex]e=0_{V}[/tex] then [tex]U[/tex] and [tex]cv+w \in U[/tex] provided that [tex]u,v\in U, c\in \mathbb{K}[/tex], then [tex]U[/tex] is a closed set under the operations of sum and scalar multiplicattion, then it is a vector space since the properties listed above are inherited from V since the elements of [tex]U[/tex] are elements of V. Then [tex]U[/tex] is a subspace of [tex]V[/tex].
Now if we know that [tex]U[/tex] is a subspace of [tex]V[/tex] then [tex]U[/tex] is a vector space, and clearly it satisfies the properties [tex]cv+w\in U[/tex] whenever [tex]v,w\in U, c\in \mathbb{K}[/tex] and [tex]0_{V}\in U[/tex].
This is an useful criteria to determine whether a given set is subspace of a vector space.
If P(A)equals one half , P(B)equals three fifths , and P(B/A) equals one sixth , find P( A/B)
Answer:
[tex]\frac{5}{36}[/tex]
Step-by-step explanation:
Given,
P(A) = [tex]\frac{1}{2}[/tex],
P(B) = [tex]\frac{3}{5}[/tex]
[tex]P(\frac{B}{A})=\frac{1}{6}[/tex]
[tex]\because P(\frac{B}{A})= \frac{P(A\cap B)}{P(A)}[/tex]
[tex]\implies \frac{P(A\cap B)}{P(A)} = \frac{1}{6}[/tex]
[tex]\frac{P(A\cap B)}{\frac{1}{2}}=\frac{1}{6}[/tex]
[tex]2P(A\cap B) = \frac{1}{6}[/tex]
[tex]\implies P(A\cap B) = \frac{1}{12}[/tex]
Now,
[tex]P(\frac{A}{B})=\frac{P(A\cap B) }{P(B)}= \frac{1/12}{3/5}=\frac{5}{36}[/tex]
Instructions for a chemical procedure state to mix salt, baking soda, and water in a 20:15:10 ratio by mass. How many grams of water would be required to make a mixture that contains 24 grams of baking soda?
Answer:
16 g of water.
Step-by-step explanation:
salt : baking soda : water = 20 : 15 : 10
If we have 24 g of baking soda that is 24/15 = 8/5 times of 15.
So by proportion the amount of water would be 10 * 8/5 = 16 grams.
The mass of water in the mixture is 16 gm
What is Ratio and Proportion ?When a number is divisible by another number then they can be written in the form of ratio p :q , When two ratios are equal they are said to be in proportion.
It is given that
salt, baking soda, and water in a 20:15:10 ratio by mass are mixed
mixture contains 24 grams of baking soda
Mass of Water = ?
Baking Soda : Water = 15 : 10
Let the mass of water is x
then the ratio is 24 : x
As both these ratios are equal
15 : 10 = 24 : x
15 / 10 = 24 / x
x = 24 * 10 / 15
x = 16 gm
Therefore the mass of water in the mixture is 16 gm.
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The formulas below are the cost and revenue functions for a company that manufactures and sells small radios. a. Use the formulas shown to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 21,000 radios are produced and sold C(x) 224,000+32x and R(x) 46x a. The company's profit function is P(x)-(Simplify your answer.)
Answer:
(a) The profit function is P(x)=14x-224,000.
(b) The company's profit at x=21000 is 70,000.
Step-by-step explanation:
Cost function is
[tex]C(x)=224,000+32x[/tex]
Revenue function is
[tex]R(x)=46x[/tex]
where, x is number of radios.
(a)
Formula for profit:
Profit = Revenue - Cost
The profit function is
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=46x-(224,000+32x)[/tex]
[tex]P(x)=46x-224,000-32x[/tex]
[tex]P(x)=14x-224,000[/tex]
The profit function is P(x)=14x-224,000.
(b)
Substitute x=21000 in the above equation to find the company's profit if 21,000 radios are produced and sold.
[tex]P(21000)=14(21000)-224,000[/tex]
[tex]P(21000)=294000-224,000[/tex]
[tex]P(21000)=70,000[/tex]
Therefore the company's profit at x=21000 is 70,000.
The profit function for a company is found by subtracting the cost function from the revenue function. Given the cost and revenue functions, the profit function simplifies to P(x) = 14x - 224,000. If 21,000 radios are sold, the company will take a loss of $56,000.
Explanation:Profit function in a company can be obtained by subtracting total cost from total revenue, it can be represented as P(x) = R(x) - C(x). Here, R(x) is the revenue function and C(x) is the cost function.
Given, the cost function of the company C(x) is 224,000 + 32x and the revenue function R(x) is 46x. Substituting these values into our profit function we get, P(x) = 46x - (224,000 + 32x), simplifying it leads to P(x) = 46x - 224,000 - 32x, which can be further simplified to P(x) = 14x - 224,000.
For part b of the question, if 21,000 radios are produced and sold, we substitute x=21,000 into the profit function. Hence, P(21000) = 14*21000 - 224,000 = -56,000. This indicates that the company will experience a loss when 21,000 radios are produced and sold.
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Convert 72degrees into radians
Answer:
72° = 1.25 radians
Step-by-step explanation:
As we know that,
[tex]1 degree = \frac{\pi}{180} radians[/tex]
Thus, [tex]72^{\circ} = 72\times\frac{\pi}{180}radians[/tex]
⇒ [tex]72^{\circ} =\frac{2\pi}{5}radians[/tex]
⇒ 72° = 1.25 radians {∵ Using π = 22÷ 7 or 3.14}
Both degrees and radians are used to measure the angle. They are units of angle.
The radius of the Earth is 6370km, the atmospheric pressure at sea level is 1 bar and the density at sea level is 1.2 kg/m^3.
Estimate the mass of the atmosphere assuming the height of the atmosphere is 11km.
Answer:
The mass of atmosphere equals [tex]6742.368\times 10^{15}kg[/tex]
Step-by-step explanation:
Since the earth can be assumed to be as sphere ,to calculate the mass of the atmosphere we need to calculate the volume of the atmosphere.
The volume of atmosphere can be found by subtracting the volume of earth from the volume of the sphere formed by envelop of atmosphere around the earth as indicated in the attached figure
Mathematically we have
[tex]V_{atmosphere}=V_{shell}-V_{earth}\\\\V_{atmosphere}=\frac{4\pi (R_{e}+h)^{3}}{3}-\frac{4\pi R_{e}^{3}}{3}\\\\V_{atmosphere}=\frac{4\pi }{3}((6370+11)^{3}-(6370)^{3})\\\\V_{atmosphere}=5618.64\times 10^{6}km^{3}\\\\\\V_{atmosphere}=5618.64\times 10^{15}m^{3}[/tex]\
Now since it is given that 1 cubic meter of atmosphere weighs 1.2 kilogram thus the mass of the whole atmosphere equals
[tex]Mass_{atmosphere}=1.2\times 5618.64\times 10^{15}kg\\\\Mass_{atmosphere}=6742.368\times 10^{15}kg[/tex]
To estimate the mass of the atmosphere, we use the formula Mass = Density × Volume. First, calculate the volume of the atmosphere using the formula for the volume of a cylinder. Then, substitute the given values into the formula and calculate the mass using the formula Mass = Density × Volume.
Explanation:To estimate the mass of the atmosphere, we can use the formula:
Mass = Density × Volume
First, we need to find the volume of the atmosphere. The height of the atmosphere is given as 11 km, so we can calculate the volume using the formula for the volume of a cylinder:
Volume = π × (radius2) × height
Next, we substitute the given values into the formula:
Volume = π × (6370 km)2 × 11 km
Finally, we calculate the mass using the formula:
Mass = Density × Volume
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Jacob made a circle-shaped poster for his geometry class.
If the radius of circle-shaped poster is 10 inches, what is the
circumference?
Use 3.14 for .
Answer: [tex]62.8\text{ inches}[/tex]
Step-by-step explanation:
The circumference of a circle is given by :-
[tex]C=2\pi r[/tex], where r is the radius of the circle.
Given : Radius of a circle = 10 inches
Then, the circumference of circle will be :_
[tex]C=2(3.14) (10)\\\\\Rightarrow\ C=62.8\text{ inches}[/tex]
Hence, the circumference of the circle will be [tex]62.8\text{ inches}[/tex]
A client who weights 176 pounds is receiving an IV infusion with esmolol hydrochloride (Brevibloc) at 48 ml/hour. The IV solution is labeled with the concentration of Brevibloc 10 mg/ml. How many mcg/kg/minute is the client receiving? (Enter numeric value only. Round to nearest whole number.) Submit
Answer:
[tex]0.1\frac{mg}{kg*min}=100 \frac{\mu g}{kg*min}[/tex]
Step-by-step explanation:
First write the weight of the client in kg, considering that 1 pound is 0.45 kg:
[tex]w=176lb* \frac{0.45kg}{1lb}=79.83kg[/tex]
Then, transform the infusion flow to ml/min, considering that 1 hour is 60 minutes:
[tex]48ml/h*\frac{1h}{60min}=0.8ml/min[/tex]
Now it is possible to calculate the to total mass flow injected to the client per minute:
[tex]0.8\frac{ml}{min}*10\frac{mg}{ml} =8mg/min[/tex]
To find the mass flow of Brevibloc injected by unit of weight of the pacient, just divide the total mass flow by the weight of the client:
[tex]8\frac{mg}{min}*\frac{1}{79.83kg}=0.1\frac{mg}{kg*min}[/tex]
In the question is not clear, but if you need the answer in micrograms/kg/minute just multiply by 1000:
[tex]0.1\frac{mg}{kg*min}*\frac{1000\mu g}{1mg}=100 \frac{\mu g}{kg*min}[/tex]
For the following function
f(x) = 5x^2 - 55x + 151
find
(a) f(4),
(b) f(-1),
(c) f(a),
(d) f(2/m)
(e) any values of x such that f(x)=1.
Answer:
(a) f(4) = 11
(b) f(-1) = 211
(c) f(a) = 5a² -55a +151
(d) f(2/m) = (151m² -110m +20)/m²
(e) x = 5 or x = 6
Step-by-step explanation:
A graphing calculator can help with function evaluation. Sometimes numerical evaluation is easier if the function is written in Horner Form:
f(x) = (5x -55)x +151
(a) f(4) = (5·4 -55)4 +151 = -35·4 +151 = -140 +151 = 11
__
(b) f(-1) = (5(-1)-55)(-1) +151 = 60 +151 = 211
__
(c) Replace x with a:
f(a) = 5a² -55a +151
__
(d) Replace x with 2/m; simplify.
f(2/m) = 5(2/m)² -55(2/m) +151 = 20/m² -110m +151
Factoring out 1/m², we have ...
f(2/m) = (151m² -110m +20)/m²
__
(e) Solving for x when f(x) = 1, we have ...
5x² -55x +151 = 1
5x² -55x +150 = 0 . . . . subtract 1
x² -11x +30 = 0 . . . . . . . divide by 5
(x -5)(x -6) = 0 . . . . . . . . factor
Values of x that make the factors (and their product) zero are ...
x = 5, x = 6 . . . . values of x such that f(x) = 1
If BC = CD and AB = 23, what is BD?
Prove that if a and b are integers, then a^2-4b egal or non-egal 2
Answer:
tex]a^2 - 4b \neq 2[/tex]
Step-by-step explanation:
We are given that a and b are integers, then we need to show that [tex]a^2 - 4b \neq 2[/tex]
Let [tex]a^2 - 4b = 2[/tex]
If a is an even integer, then it can be written as [tex]a = 2c[/tex], then,
[tex]a^2 - 4b = 2\\(2c)^2 - 4b =2\\4(c^2 -b) = 2\\(c^2 -b) =\frac{1}{2}[/tex]
RHS is a fraction but LHS can never be a fraction, thus it is impossible.
If a is an odd integer, then it can be written as [tex]a = 2c+1[/tex], then,
[tex]a^2 - 4b = 2\\(2c+1)^2 - 4b =2\\4(c^2+c-b) = 2\\(c^2+c-b) =\frac{1}{4}[/tex]
RHS is a fraction but LHS can never be a fraction, thus it is impossible.
Thus, our assumption was wrong and [tex]a^2 - 4b \neq 2[/tex].
To demonstrate that a2 - 4b cannot equal 2 for integers a and b, we can argue based on the discriminant of a quadratic equation, which should be non-positive for the equation to have one or no real roots.
In mathematics, particularly algebra, understanding the properties of polynomial equations is fundamental. When we consider the quadratic equation X^2 + aX + b = 0, it can have either one or no real roots, which is determined by its discriminant, denoted as Det = a^2 - 4b. Now, the condition for a quadratic equation to have a single (degenerate) real root or no real roots at all is that the discriminant must be non-positive.
To prove that a22 - 4b
qq 2 for all integers a and b, we can reason that if a2 - 4b were equal to 2, the quadratic equation would have two distinct real roots, which contradicts the earlier statement that the discriminant must be non-positive for it to have one or no real roots. Therefore, this proves that a2 - 4b cannot be equal to 2; hence a2 - 4b
nn2 for all integers a and b.
Problem 8 - Simple and Compound Interest
At an effective annual rate of interest of 5.3%, the present value of $7425.70 due in t years is $3250. Determine t
Problem 4 - Simple and Compound Interest
How much would you invest today to have $9500 in 8 years if the effective annual rate of interest is 4%?
Problem 8 - Simple and Compound Interest
At an effective annual rate of interest of 5.3%, the present value of $7425.70 due in t years is $3250. Determine t ?
Answer:
P8) [tex]t=7.02 years[/tex]
P4) Today you have to invest $6941.55
P8) Is the same P8 above
Step-by-step explanation:
P8) First of all, we can list the knowns [tex]VP=7425.70[/tex], [tex]I=3250[/tex] and [tex]i=5.3[/tex]%, so we use [tex]VF=VP+I=7425.70+3250=10675.70[/tex] then we use [tex]t=\frac{ln(VF/VP)}{ln(1+i)}=\frac{ln(10675.70/7425.70)}{ln(1+0.053)} =\frac{0.363}{0.051}=7.02 years[/tex]
P4) First of all, we can list the knowns [tex]VF=9500[/tex], [tex]t=8[/tex] and [tex]i=4[/tex]%, so we use [tex]VP=\frac{VF}{(1+i)^{t} } =\frac{9500}{(1+0.04)^{8} } =6941.55[/tex]
P8) Is the same P8 above
Find the area of the triangle
Answer:
A ≈ 14.079 square units
Step-by-step explanation:
Area of a triangle is one half the base times the height.
A = ½ bh
A = ½ (10) (2x)
A = 10x
We need to find the value of x.
Starting with the triangle on the left, use Pythagorean theorem to find the length of the base.
(3x)² = (2x)² + a²
9x² = 4x² + a²
a² = 5x²
a = x√5
Repeat for the triangle on the right:
(x + 6)² = (2x)² + b²
x² + 12x + 36 = 4x² + b²
b² = -3x² + 12x + 36
The two bases add up to 10:
a + b = 10
Subtract a from both sides, then square both sides:
b = 10 − a
b² = 100 − 20a + a²
Substitute and simplify:
-3x² + 12x + 36 = 100 − 20(x√5) + 5x²
0 = 64 − (12 + 20√5) x + 8x²
0 = 2x² − (3 + 5√5) x + 16
Solve with quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ (3 + 5√5) ± √((-(3 + 5√5))² − 4(2)(16)) ] / 2(2)
x = [ (3 + 5√5) ± √(9 + 30√5 + 125 − 128) ] / 4
x = [ (3 + 5√5) ± √(6 + 30√5) ] / 4
x ≈ 1.4079, 5.6823
If we substitute 5.6823 into our a and b equations, we find that a = 12.706 and b = 7.322, which add up to 20.028, not 10.
So x ≈ 1.4079.
Therefore the area is:
A ≈ 14.079
what’s the answer to k and m ? please explain how you found the answer .
Answer:
Step-by-step explanation:
So what multiplied by what is equal to 0.64? Well you know that 8*8 is equal to positive 64, and since 0.64 is just 64 moved down two decimal spaces, you do the same with 8. So For k, it's 0.8
For m, you do the same. So what multiplied by what is equal to 0.25? Well you know that 5*5 is equal to positive 25, and since 0.25 is just 25 moved down two decimal spaces, you do the same with 5. So For m, it's 0.5.
Let a graph have vertices {L, M, N, O, P, Q, R, S} and edge set {{L,R}, {M,P}, {M,Q}, {N,Q}, {P,R}, {Q,S}, {R,S}} .
a. What is the degree of vertex P?
b.What is the degree of vertex O?
c.How many components does the graph have?
Answer:
a) The degree of vertex P is 2.
b) The degree of vertex O is 0.
c) The graph has 2 components.
Step-by-step explanation:
a) The edges that have P as a vertice are {M,P} and {P,R}.
b) There is no edge with extreme point O.
c) One of the components is the one with the only vertex as O and has no edges. The other component is the one with the rest of the vertices and all the edges described.
The file has a realization of the graph.
The Call First cell phone company charges 535 per month and an additional 50.16 for each text message sent during the month. Another cell phone company, Cellular Plus, charges $45 per month and an additional $0.08 for each text message sent during the month a. How many text messages would have to be sent in a month to make both plans cost the same?
Answer:
125 text messages.
Step-by-step explanation:
Let x represent number of text messages.
We have been given that the Call First cell phone company charges $35 per month and an additional $0.16 for each text message sent during the month.
The cost of sending x text messages using call first would be [tex]0.16x[/tex].
The total cost of sending x text messages using call first would be [tex]0.16x+35[/tex].
Cellular Plus, charges $45 per month and an additional $0.08 for each text message sent during the month.
The cost of sending x text messages using cellular plus would be [tex]0.08x[/tex].
The total cost of sending x text messages using cellular plus would be [tex]0.08x+45[/tex].
Now, we will equate both expressions to solve for x as:
[tex]0.16x+35=0.08x+45[/tex]
[tex]0.16x-0.08x+35=0.08x-0.08x+45[/tex]
[tex]0.08x+35=45[/tex]
[tex]0.08x+35-35=45-35[/tex]
[tex]0.08x=10[/tex]
[tex]\frac{0.08x}{0.08}=\frac{10}{0.08}[/tex]
[tex]x=125[/tex]
Therefore, 125 text messages would have to be sent in a month to make both plans cost the same.
A sample of iron ore has a density of 7.87 what is its mass? Show all of your work. If it measures 7.5 cm x 2.53 em x 7.15 cm,
Answer:
Mass=1068gr
Step-by-step explanation:
Volume= 7.5 cm x 2.53 cm x 7.15 cm=135.7cm^3
Density=7.87gr/cm^3
Mass=Density*Volume=135.7*7.87=1068gr
Fill in the table in the photo
Answer:
see the attachment
Step-by-step explanation:
If the growth is 7 feet in 2 weeks and the rate is constant, then it will be half that in one week, or 3.5 feet per week. At week 3, it will be 3.5 feet more than at week 2. The table below shows this progression.
The point (0, 0) means there was no measurable growth when time was starting to be measured (at week 0).
Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m. The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do. What information is missing that might contradict this claim?
Answer: The conclusion cannot be confirmed unless we have the statistic of the men.
Step-by-step explanation: Only looking at the number of women in both times 8 am and 10 am, will not determine if the men prefer of do no prefer earlier classes. We would need the men's statistics as well for both time slots. There may be more men among the 8 am slot e.g 25 women and 30 men. There is incomplete information to come up with a sound conclusion.
Determine the angles made by the vector V= (-35)i + (-41)j with the positive x-and y-axes. Write the unit vector n in the direction of V. Answers: ex= 9,0y i n =
Answer:
angle made by the vector with positive x axis,
[tex]\theta\ =\ 49.51^o[/tex]
the angle by the positive direction of y axis,
[tex]\alpha\ =\ 40.48^o[/tex]
unit vector in the direction of the given vector,
[tex]\hat{n}\ =\ \dfrac{(-35)i+(-41)j}{53.9}[/tex]
Step-by-step explanation:
Given vector is
[tex]\vec{V}=\ (-35)i\ +\ (-41)j[/tex]
we have to calculate the angle made by the vector with positive x and y axis,
The angle made by the vector with positive x axis can be given by,
[tex]tan\theta\ =\ \dfrac{-41}{-35}[/tex]
[tex]=>\ \theta\ =\ tan^{-1}\dfrac{-41}{-35}[/tex]
[tex]=>\ \theta\ =\ 49.51^o[/tex]
And the angle by the positive direction of y axis can be given by
[tex]\alpha\ =\ 90^o-\theta[/tex]
[tex]=\ 90^o-49.51^o[/tex]
[tex]=\ 40.48^o[/tex]
Now, we will calculate the unit vector in the direction of the given vector.
So,
[tex]\hat{n}\ =\ \dfrac{\vec{A}}{|\vec{A}|}[/tex]
[tex]=\ \dfrac{(-35i)+(-41)j}{\sqrt{(-35)^2+(-41)^2}}[/tex]
[tex]=\ \dfrac{(-35)i+(-41)j}{53.9}[/tex]
how to make a number line from -6.2 to -9.1
Answer:
3.1
Step-by-step explanation:
because u have to take away the - sign if it is two negatives :3
Step-by-step explanation:
you draw a line (don't forget to put arrows on the end) then you put the point farthest to the left :(-9.1) and the point farthest to the right (-6.2).
in between these points you add the ponts -9,-8,-7-,6 respectively.
The concentration of DDT (C14H9Cl5), in milligrams per liter, is:
(1) a nominal variable
(2) an ordinal variable
(3) an interval variable
(4) a ratio variable.
Answer:
The correct option is 4) a ratio variable.
Step-by-step explanation:
Consider the provided information.
Nominal variables are pertaining to names or It merely name differences, it is a qualitative variables.
Ordinal variable: It is a rank-order observations in which order matters but difference between the value doesn't matters. It is a qualitative variables.
Interval variable: It is useful if the difference between two values is meaningful. It is a quantitative variables.
Ratio variable: this variable has all the properties of an interval variable, also it has a clear definition of 0.0. It is a quantitative variables.
Now consider the provided information.
The concentration is in milligrams per liter which is a quantitative variable.
Among the provided options only ratio variable and interval variable is quantitative variable. So option A and B are incorrect.
Since the milligrams per liter can be zero point which is not the characteristic of interval scale. Thus, the option C is incorrect.
The zero point is characteristic of ratio variable. Thus, the concentration of DDT (C14H9Cl5), in milligrams per liter, is ratio variable.
Hence, the correct option is 4) a ratio variable.
Final answer:
The concentration of DDT in milligrams per liter is best described as a ratio variable, as it is measured on a numeric scale that includes a true zero, allowing for meaningful comparisons and arithmetic operations.
Explanation:
The concentration of DDT, which is a chemical compound with the formula C14H9Cl5, in a given volume of solution is a measure that can be categorized using levels of measurement in statistics. In this context, concentration is measured in milligrams per liter (mg/L), which is a unit that indicates the mass of the substance (DDT) in a specific volume of the liquid (water).
Among the four types of variables listed (nominal, ordinal, interval, and ratio), the concentration of DDT in mg/L is best described as a ratio variable. This is because it has a true zero point (0 mg/L indicates the absence of DDT), and the difference between any two concentrations has a meaningful interpretation. Additionally, you can perform a full range of arithmetic operations on ratio variables.
Nominal variables are categorical and do not have a numeric order. Ordinal variables are categorical with a clear order, whereas interval variables have a numeric scale without a true zero. However, for measurements like concentration of DDT, that have a true zero and are continuous, the appropriate level of measurement is the ratio level.
Mr. and Mrs. Wong purchased their new house for $350,000. They made a down payment of 20%, and amortized the rest over 30 years. If the interest rate is 4.2%, which of the following is their correct monthly mortgage payment?
Answer:
$1,369.25
Step-by-step explanation:
Mr. and Mrs. Wong purchased their new house for $350,000.
They made a down payment of 20%
Down payment = 20% of 350000
= $70,000
Loan amount, P = $350,000 - $70,000
= $280,000
Rate of interest, r = 4.2% or 0.042
Time, t = 30 years
Number of period, n = 12 ( monthly )
Formula: [tex]E=\dfrac{P\cdot \frac{r}{n}}{1-(1+\frac{r}{n})^{-n\cdot t}}[/tex]
Substitute the values into formula
[tex]E=\dfrac{280000\cdot \frac{0.042}{12}}{1-(1+\frac{0.042}{12})^{-12\cdot 30}}[/tex]
E = $1,369.25
Hence, The monthly payment for their mortgage will be $1,369.25