Answer:
Step-by-step explanation:
Decay of carbon - 14 is exponential in nature . It decays as follows .
[tex]N=N_0e^{-\lambda t}[/tex] λ is called decay constant .
λ = .693 / T where T is half life .
Half life of carbon-14 is 5700 years
λ = .693 / T
= .693 / 5700
= 12.158 x 10⁻⁵ year⁻¹
[tex]N=N_0e^{-\lambda t}[/tex]
N = .71 N₀
[tex].71 N_0 =N_0e^{-\lambda t}[/tex]
[tex].71 =e^{-\lambda t}[/tex]
Taking ln on both sides
ln .71 = - λ t
ln .71 = - 12.158 x 10⁻⁵ t
-0.3425 = - 12.158 x 10⁻⁵ t
t = .3425 / 12.158 x 10⁻⁵
2817 years .
which terms are like terms in the following expression ? 6x + 8xy - 3x + 9y + 4x^2
Answer:
[tex]\Large \boxed{{6x \ \mathrm{and} \ -3x}}[/tex]
Step-by-step explanation:
Like terms have identical variables and exponents, the coefficients don’t have to be the same.
The like terms from the expression are 6x and -3x.
Step-by-step explanation:
Hey, there!!
6x and -3x are like terms.
Like terms in algebraic terms are those terms which has same variable or exponents. In This expression "6x+8xy-3x+9y4x^2"
6x and -3x has "x" common in them so, The answer is 6x and -3x.
Hope it helps..
Complete each equation with a number that makes it true. 5⋅______=15 4⋅______=32 6⋅______=9 12⋅______=3
Answer: blank 1: 3 Blank 2: 8 blank 3: 1.5 blank 4: 0.25
Step-by-step explanation:
5 times 8=15
4 times 8=32
6 times 1.5=9
12 times 0.25=3
The complete equation is
5⋅____3__=15
4⋅___8___=32
6⋅___1.5___=9
12⋅__0.25____=3
What is Multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Multiplication Formula
The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:
Multiplicand: The first number (factor).Multiplier: The second number (factor).Product: The final result after multiplying the multiplicand and multiplier.Multiplication symbol: '×' (which connects the entire expression)5 * 3=154 * 8=326 * 1.5=912 * 0.25=3Learn more about multiplication here:
https://brainly.com/question/5992872
#SPJ2
log 7 (x^2 + 11) = log 7 15
Answer:
x = ±2
Step-by-step explanation:
log 7 (x^2 + 11) = log 7 15
We know that log a ( b) = log a(c) means b =c
x^2 + 11 = 15
Subtract 11 from each side
x^2 = 15-11
x^2 =4
Take the square root of each side
sqrt(x^2) =±sqrt(4)
x = ±2
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework?
Answer:
Step-by-step explanation:
½ of 5¼
½×(21/4)
=21/8
=2⅝ hours
Answer:
2 5/8
Step-by-step explanation:
you would divide 5 1/4 by 2 :
5 divided by 2 =2 1/2
1/4 divided by 2=1/8
then make the numbers have the same denomanator
1/2, 2/4, 4/8
1/8,
then you add
2 4/8+1/8=2 5/8
Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?
0riginal break even point:
285000/ 60/35 = $166,250
New break even point = new fixed costs / ( selling price - variable cost/ selling price)
New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60
300,900 / 60-30.50/60 = $612,000
The new break even point increases.
Cases Prudence has a special (cubic) die. The values on its face are the integers from 1 to 6, but they are not arranged ae in a normal die. When Prudence first tosses the die, the sum of the values on the four side faces is 15. In her second toss, the sum of these values is 12. Find what value appears in the face opposite 6 on Prudence’s special die. (Hint: what are possible values for the top and bottom face when the sum of the side faces is 12).
Answer: 3
Step-by-step explanation:
first, we know that:
1 + 2 + 3 + 4 +5 +6 = 21
Now, which two numbers we should take out in order to have 15?
we can remove the 2 and the 4, or the 1 and the 5.
so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)
in the other arrange, we have that removing two numbers we should get 12.
in order to reach 12, we should remove two numbers that add 9 together.
those can be 4 and 5, or 6 and 3.
Now, notice that in the first restriction we have that:
Or 2 and 4 are opposite,
or 1 and 5 are opposite.
So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.
Then we can affirm that the value that appears in the face opposite to the 6, is the 3.
The graph of the function f(x) = (x − 3)(x + 1) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answer:
x < -1
Step-by-step explanation:
Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.
all real values of x where x < -1
How many pepperoni pizzas did they buy if they bought 6 cheese pizzas
Answer:
Question is incomplete but use below
Step-by-step explanation:
you can do total = (price of cheese pizza) ( amount of cheese pizzas bought)+(price of pepperoni pizza) ( amount of pepperoni pizzas bought)
At Jefferson Middle School, eighty-two students were asked which sports they plan to participate in for the coming year. Twenty students plan to participate in track and cross country; six students in cross country and basketball; and eight students in track and basketball. Twelve students plan to participate in all three sports. A total of thirty students plan to participate in basketball, and a total of forty students plan to participate in cross country. Ten students don't plan to participate in any of the three sports. How many students plan to just participate in cross country? 2 4 40 30
Answer:
40
Step-by-step explanation:
In the question only lies the answer:
"and a total of forty students plan to participate in cross country."
Answer:
2
Step-by-step explanation:
2
Find the measure of F. A. 44 B. 88 C. 90 D. 46
Answer:
A. 44º
Step-by-step explanation:
The sum of internal angles in a triangle is equal to 180 degrees, whereas the sum for a square is equal to 360 degrees. Given that three triangles depicted on figure constructs a square, it is to conclude that each is an isosceles triangle. The following relations are presented:
1) [tex]e + 92^{\circ} = 180^{\circ}[/tex] Given
2) [tex]a = b[/tex], [tex]c = d[/tex] Given
3) [tex]a + b + 92^{\circ} = 180^{\circ}[/tex] Given.
4) [tex]c + d + e = 180^{\circ}[/tex] Given.
5) [tex]b + c = 90^{\circ}[/tex] Given.
6) [tex]2\cdot a + 92^{\circ} = 180^{\circ}[/tex] 2) in 3)
7) [tex]a = 44^{\circ}[/tex] Algebra
8) [tex]b = 44^{\circ}[/tex] By 2)
9) [tex]b= f[/tex] Alternate internior angles.
10) [tex]f = 44^{\circ}[/tex] By 8). Result
Hence, the answer is A.
area please it's easy plzzzzzzzzzz
a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.
Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²
The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²
b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.
Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,
Area of Striped Region : 40 - 22 = 18 m²
A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table. A 2-column table has 5 rows. The first column is labeled Color with entries blue, green, red, orange, yellow. The second column is labeled Number with entries 1, 2, 0, 4, 3. Which statements are true about Yuri’s experiment? Select three options. The theoretical probability of spinning any one of the five colors is 20%. The experimental probability of spinning blue is One-fifth. The theoretical probability of spinning green is equal to the experimental probability of spinning green. The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
Answer:
A. The theoretical probability of spinning any one of the five colors is 20%.
C. The theoretical probability of spinning green is equal to the experimental probability of spinning green.
E. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
These are the answers on edg 2020, just took the test.
Step-by-step explanation:
Answer:
a, c, e,
Step-by-step explanation:
:)
Complete parts (a) through (c) below.
(a) Determine the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.
(b) Determine the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 level of significance based on a sample size of n = 20.
(c) Determine the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.
Answer:
(a) 1.341
(b) -2.539
(c) -2.160 and 2.160
Step-by-step explanation:
(a) We have to find the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%
Now, looking in the t table with P = 10% and [tex]\nu[/tex] = 15, we get the critical value of 1.341.
(b) We have to find the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%
Now, looking in the t table with P = 1% and [tex]\nu[/tex] = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.
(c) We have to find the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is [tex]\frac{0.05}{2}[/tex] is 0.025, i.e. P = 2.5%.
Now, looking in the t table with P = 2.5% and [tex]\nu[/tex] = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.
g If the events A and B are independent with P( A) = 0.35 and P( B) = 0.45, then the probability that both events will occur simultaneously is:
Answer:
0.1575.
Step-by-step explanation:
Here, as they are independent, we multiply the probabilities:
P( A and B) = 0.35*0.45
= 0.1575.
The probability that both events will occur simultaneously is 0.1575.
Given that, the events A and B are independent with P( A) = 0.35 and P( B) = 0.45.
What is independent probability?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
Since, the events A and B are independent
We have P(A and B)
= P(A) × P(B)
= 0.35 × 0.45
= 0.1575
Hence, the probability that both events will occur simultaneously is 0.1575.
Learn more about the independent probability here:
https://brainly.com/question/27987662.
#SPJ5
3.85∙47.3+52.7∙3.85 PLSSSSS HELP
Answer:
385
Step-by-step explanation:
the box plots shows the price for two different brands of shoes
Answer:
A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.
Step-by-step explanation:
The most appropriate measure that can be used to compare the SPREAD of the data of the 2 brands plotted on a box plot, is the Interquartile range (IQR).
Interquartile range is the difference between Q3 and Q1.
Q3 is the value which lies at the end of the rectangular box, while the Q1 lies at the beginning of the box.
From the box plot given,
IQR for brand A = 80 - 70 = $10
IQR for brand B = 50 - 25 = $25
Therefore, the correct option is "A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25."
10 points plssssss!!!
Answer:
A. rectangle
B. any of triangle, quadrilateral, pentagon, hexagon
Step-by-step explanation:
A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.
__
B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...
trianglequadrilateralpentagonhexagon5(y–3.8)=4.7(y–4) help help
Answer:
y = 2/3 or 0.667Step-by-step explanation:
5(y–3.8)=4.7(y–4)
Expand the terms in the bracket
That's
5y - 19 = 4.7y - 18.8
Group like terms
5y - 4.7y = 19 - 18.8
0.3y = 0.2
Divide both sides by 0.3
We have the final answer as
y = 2/3 or 0.667Hope this helps you
Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy
Answer:
Charlie: 5 + xDanny: x - 8Eric: x × 3Find an equation of the plane through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1). Do this problem in the standard way.
Answer:
x+5y+z = 25Step-by-step explanation:
Given a plane passing through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1), the equation of the plane can be expressed generally as;
a(x-x₀)+b(y-y₀)+c(z-z₀) = 0 where (x₀, y₀, z₀) is the point on the plane and (a, b,c) is the normal vector perpendicular to the plane i.e (1,5,1)
Given the point P (1, 5, -1) and the normal vector n(1, 5, 1)
x₀ = 1, y₀ =5, z₀ = -1, a = 1, b = 5 and c = 1
Substituting this point in the formula we will have;
a(x-x₀)+b(y-y₀)+c(z-z₀) = 0
1(x-1)+5(y-5)+1(z-(-1)) = 0
(x-1)+5(y-5)+(z+1) = 0
x-1+5y-25+z+1 = 0
x+5y+z-1-25+1 = 0
x+5y+z-25 = 0
x+5y+z = 25
The final expression gives the equation of the plane.
square root of 49/64 answered as a fraction
Answer:
Hey there!
That would be 7/8
Let me know if this helps :)
I NEED HELP WITH THESE 4 ASAP
Answer:
I'm confused by this. What do they mean by prove?
Step-by-step explanation:
Which of the following is the graph of the quadratic parent function
This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Answer:
9 m
Step-by-step explanation:
Given that
Width of rectangular flower garden, w = 4 m
Perimeter of rectangular flower garden, p = 26 m
To find:
Length of Lisa's flower garden = ?
Solution:
First of all, let us understand perimeter, length and width of a rectangle.
Let ABCD be a rectangle. Please refer to the attached image.
Opposite sides of a rectangle are equal to each other.
AB = CD = Length
Let the length be [tex]l[/tex] m.
BC = DA = Width = 4 m
Perimeter of a closed image is equal to the sum of all the sides of the image.
So, perimeter of ABCD:
[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]
[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]
If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)).
A(t) = 100t^2 + 500t + 625
3,025 square pixels
Answer:
A(t) equals 100t²+ 500t + 625.
The area of the square image after 3 seconds is 3,025 square pixels.
Calculate, correct to one decimal plice
the acute angle between the lines
3x - 4y + 5 = 0 and 2x + 3y -1 = 0
A. 70.69
B. 50.2
C. 39.8
D. 19.4
Answer:
A. 70.69 is the correct answer.
Step-by-step explanation:
Given:
Two lines:
[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]
To find:
Angle between the two lines = ?
Solution:
Acute Angle between two lines can be found by using the below formula:
[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]
Where [tex]\theta[/tex] is the acute angle between two lines.
[tex]m_1, m_2[/tex] are the slopes of two lines.
Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:
[tex]m = -\dfrac{a}{b }[/tex]
So,
[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]
[tex]m_2 = -\dfrac{2}{ 3}[/tex]
Putting the values in the formula:
[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]
So, correct answer is A. 70.69
A department store offers two promotions. Promotion A says, "Buy one pair of shoes, get the second pair for half the price." Promotion B says, "Buy one pair of shoes, get $10 off the second pair." Jane wants to buy two pairs of shoes that cost $30 each. She can only use one of the promotions, A or B. Jane decides to use the promotion that will save her the most money. How many dollars does Jane save by picking one promotion over the other? (For example, if Jane spends $150 on her purchase by using one promotion and $100 on her purchase by using the other promotion, she saves $150-100=50$ dollars by using the second promotion over the first.)
Answer:
$5
Step-by-step explanation:
Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.
Please help me understand this question!
Answer:
C
Step-by-step explanation:
The first sentence basically sets up the equation which is given, so we can read it for knowledge but it is not crucial to solve the problem.
We start here:
we are given: $120 - 0.2($120)
= 120 - (0.2)(120) (factoring out 120)
= 120 (1 - 0.2)
= 120 (0.8)
= 0.8 (120) (answer c)
football team, won 35 out of 39 games over a period of 4 years. if they keep winning pace, predict how many games you would expect them to win over the next 78 football games
Answer:
70
Step-by-step explanation:
If the team continues with same pace, they expected wins as per previous ratio:
35/39*78 = 70Expected wins 70 out of 78 games
