The half-life of the substance is of 10.31 years.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
a sample of a radioactive substance decayed to 93% of its original amount after a year.
The half-life is t for which:
exp(-0.067 t) = (0.5)
ln(0.5) = -0.067 t
t = 10.31 years.
Hence the half-life of the substance is of 10.31 years.
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4. Make Sense and Persevere What are the values of x and y if T(-2,7)(x, y) = (3,-1)
Answer:i dont now
Step-by-step explanation:
I SAID I DONT NOW
Helppp me please please
The slopes of both equations are different. Then the lines are neither parallel nor perpendicular. Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equations of the line are given as,
y - (2/5)x = 1
y = (2/5)x + 1
25y + 10x = 50
y = -(2/5)x + 2
The slopes of both equations are different. Then the lines are neither parallel nor perpendicular. Then the correct option is A.
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Find the measure of angle 1
Answer:
b
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180° , that is
∠ 1 + 92° + 30° = 180°
∠ 1 + 122° = 180° ( subtract 122° from both sides )
∠ 1 = 58°
Answer:
[tex]\huge\boxed{\sf < 1 = 58\°}[/tex]
Step-by-step explanation:
Statement:Internal angles of a triangle add up to 180 degrees.Solution:So,
30 + 92 + ∠1 = 180
122 + ∠1 = 180
Subtract 122 to both sides
∠1 = 180 - 122
∠1 = 58°[tex]\rule[225]{225}{2}[/tex]
What words are infinitives?
Answer:
Infinitives are a special form of verbs that can be used as a noun, adjective, or adverb. They are usually made by adding the word to before the base verb, and they can be useful when discussing actions without actually doing the action, such as “I want to go home,” or “To err is human.”
Step-by-step explanation:
The purpose of infinitives is to discuss an action in general instead of a specific instance of the action being done. For example, take a look at these two sentences:
I need to win.
Today, we win.
The first sentence uses the infinitive form of the verb win as a noun; the main verb of the sentence is actually “need.” The second sentence uses the standard form of win as an actionable verb. In the first sentence with the infinitive, the action of “winning” is not actually done; the sentence simply discusses the idea of winning. The second sentence, however, describes the action of winning.
Write an equivalent unit rate to eating 3 pieces of popcorn in 1/5 of a minute ____ pieces of popcorn per minute
Answer: 15
Step-by-step explanation:
slow eater lol.
in one fifth of a minute, they ate 3 pieces. so add the other four fifths, 3 + 3 + 3 + 3 + 3, and youll get 15. easier to just multiply tho, 1/5 is 3, so 5/5 would be 3(5) = 15. hope this helps
Jill is taking her friend to lunch. The meal costs $42 and she must pay 6% sales tax. Her
service was great so she wants to leave a 20% tip. What is the final cost of the meal?
what shape is the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base?
The shape of the cross section is a triangle. It is always triangle if the triangular pyramid sliced from any side perpendicularly to its base. See the picture in the attachment!
What is a triangular pyramid?A pyramid is a polyhedron that has one base and lateral faces with the vertex at the top of the pyramid. The shape of lateral faces is always a triangle. While, the shape of the base varies and is used to name the pyramid.
A triangular pyramid is a pyramid with a triangular base. It has three lateral faces.
If a triangular pyramid is sliced by a plane from any side that is perpendicular to its base, the cross section formed will be a triangle. One line is at the base and two lines are at the lateral faces. See the picture in the attachment!
Hence, the cross section formed by the slicing is a triangle.
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how many different truth tables of compound propositions are there that involve the propositional variables p and q?
There are 16 different truth tables of compound propositions are there that involve the propositional variables p and q
What do you mean by compound proposition?
A truth table for compound propositions reveals the conditions under which the compound assertion is true. This uses more than one of the logical operators "and," "or," "negation," etc., but otherwise is identical to basic truth tables for these logical operators.
The variety of truth tables indicates the range of p and q-based functions that are possible.
Now that there are two propositions for which we are creating truth tables, p and q, any truth table will have four rows.
Each of these four rows can have a value of 0 or 1, hence there are a total of [tex]2^{4}[/tex]=16 possible ways in which these four rows can be given values.
Therefore, there are 16 different truth tables of compound propositions are there that involve the propositional variables p and q
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Use completing the square to solve the quadraic equation. Show your work using completing the square. -4x² + 9x + 10 = 0
Answer:
[tex] x = \dfrac{9}{8} \pm \dfrac{\sqrt{241}}{8} [/tex]
Step-by-step explanation:
[tex] x^2 + \dfrac{9}{-4}x + \dfrac{81}{64}= \dfrac{5}{2} + \dfrac{81}{64} [/tex]
[tex] \dfrac{-4x^2}{-4} + \dfrac{9x}{-4} = \dfrac{-10}{-4} [/tex]
[tex] x^2 + \dfrac{9}{-4}x + \dfrac{81}{64} = \dfrac{5}{2} + \dfrac{81}{64} [/tex]
[tex] (x - \dfrac{9}{8})^2 = \dfrac{241}{64} [/tex]
[tex] x - \dfrac{9}{8} = \pm\sqrt{\frac{241}{64}} [/tex]
[tex] x = \dfrac{9}{8} \pm \dfrac{\sqrt{241}}{8} [/tex]
For a project in her Geometry class, Scarlett uses a mirror on the ground to measure the height of her school building. She walks a distance of 11.25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. She then steps 0.9 meters to the other side of the mirror, until she can see the top of the school clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.55 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
By the use of a mirror, the school is 19.38 meters tall
How to determine the height of the school?From the question, we have the following parameters that can be used in our computation:
Center = xDistance walked from the school = 11.25 metersDistance walked to the other side = 0.9 metersDistance from her eyes to the ground = 1.55 meters.From the above parameters, we have the following equivalent ratio
Distance walked from the school : Height of the school = Distance walked to the other side : Distance from her eyes to the ground
Substitute the known values in the above equation, so, we have the following representation
11.25 : Height of the school = 0.9 : 1.55
Express as fraction
Height of the school/11.25 = 1.55/0.9
So, we have
Height of the school = 11.25 * 1.55/0.9
Evaluate
Height of the school = 19.38
Hence, the height of the school is 19.38 meters
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The ratio of blueberries to strawberries in a muffin mix is 3:2. If a recipe calls for 5 cups of blueberries, how many cups of strawberries will be needed?
The number of cups of strawberries that will be needed is 10/3
How to determine how many cups of strawberries will be needed?From the question, we have the following parameters that can be used in our computation:
Ratio = 3 : 2
This ratio means that
Ratio = blueberries : strawberries
Substitute the known values in the above equation, so, we have the following representation
blueberries : strawberries = 3 : 2
Also, from the question, we have
blueberries = 5
This means that
5 : strawberries = 3 : 2
So, we have
strawberries/5 = 2/3
Multiply both sides by 5
strawberries = 10/3
Hence. strawberries will be 10/3 cups
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graph the line of the equation that passes through the point (2,3) and has the slope of "-2/3"
Answer:
y = -2/3x + 13/3
Step-by-step explanation:
y = mx + c
m = -2/3
y = -2/3x + c
Put in your point (2,3):
3 = -2/3 (2) + c
3 = -4/3 + c
3 + 4/3 = c
13/3 = c
so
y = -2/3x + 13/3
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A 6x +35 6x +35
D
-6x + 35-62-35
-6x +35-6x +35
6z+35-6z - 35
Answer: The equation that has infinitely many solutions is -6x + 35 = -6x + 35
How to determine the equation?
An equation that has infinitely many solutions is represented as:
ax + b = ax + b
The above means that both sides of the equations are the same
From the list of options, we have:
-6x + 35 = -6x + 35
Both sides of the equations are the same
Hence, the equation that has infinitely many solutions is -6x + 35 = -6x + 35
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Step-by-step explanation:
suppose that all of the 1000 first-year students at a certain college are enrolled in a math or an english course. suppose 400 are taking both math and english and 600 are taking english. how many are taking a math course?
As per the set theory, the number of student who take math course is 800
Set:
In math, set means an organized collection of objects and can be represented in set-builder form or roster form.
Given,
Here we know that suppose that all of the 1000 first-year students at a certain college are enrolled in a math or an English course. suppose 400 are taking both math and English and 600 are taking English.
Now, we need to find the number of students who take math course.
While looking into the given question we have identified that,
Total Number of students = 1000
Number of students in both course = 400
Number of students taking English = 600
Then the number of students who take math course is calculated as
=> 1000 - 600 + 400
=> 800
Therefore, the resulting number of students is 800.
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WILL GIVE BRAINLIEST Walter is reading a book for English class. He records the number of pages, p, he reads as a function of the time, t, in hours, as shown. t p(t)
Answer:
39.2
Step-by-step explanation:
Avg ROC = [tex]\frac{f(b) - f(a)}{b-a} \\[/tex]
Thus
a = 0
b = 2.5
Avg ROC = [tex]\frac{98 - 0}{2.5-0} \\[/tex]
Avg ROC = 39.2
PLEASE I NEED THIS QUICKLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve the following equation for B. Be sure to take into account whether a letter is capitalized or not F=-m+B/q³
After solving the given expression → F = - m + B/q³ for [B], we get -
B = q³(F + M).
What is an expression? What is a expression? What is a mathematical equation? A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the following equation -
F = - m + B/q³
We have the following equation -
F = - m + B/q³
On solving for [B], we get -
F + M = B/q³
B = q³(F + M)
Therefore, the given expression after solving for [B], we get -
B = q³(F + M).
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one million photons are detected. what is the expected number of photons in a 1- mmmm -wide interval at xx
The expected number of photons are [tex]N=1[/tex] × [tex]10^{3} m^{2}[/tex].
What are photons?
To put it simply, photons are basic subatomic particles that carry the electromagnetic force (and so much more). The photon is also the "quantum," or basic unit, of electromagnetic radiation.
Photons are all around us: Photons make up the light coming from the screen you're looking at, the X-rays doctors use to see bones, the radio in a car that sends out its signal, and the magnets on a refrigerator that support themselves.
Given: Total number of photons = 1 million
The graph represents the probability density of a photon being found (detected) along the horizontal x- axis.
Now, checking the graph, we will find that:
At x = 0.5, the probability of finding a photon is 1.
To get the probability density at 1 mm wide at the given x value, we will simply multiply the probability with the area under curve as follows:
[tex]P(x=0.5)[/tex] × area under curve
= [tex]1[/tex] × [tex]1[/tex] × [tex]10^{-3} m^{2}[/tex]
Now, we will get the expected number of photons as follows:
N = number of photons × area under curve
[tex]N=1[/tex] × [tex]10^{6}[/tex] × [tex]1[/tex] × [tex]10^{-3}[/tex]
[tex]N=1[/tex] × [tex]10^{3} m^{2}[/tex]
Hence, the expected number of photons are [tex]N=1[/tex] × [tex]10^{3} m^{2}[/tex].
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Louis divides a 0.45-mile path into 5 equal sections for volunteers cleaning the path. He uses 0.45 divided by 5 to find the length of each section of the path.
Answer:
That's correct! Dividing the 0.45-mile path into 5 equal sections means that each section will be 0.45/5 = 0.09 miles long.
The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel.Below are the data collected and the regression equation.Diameter Strength200.1 813.7210.1 785.3220.1 960.4230.1 1118.0240.0 1076.2Strength = -941.6992 + 8.5988*Diametera)The predicted y-hat value for a diameter of 201 is 864. Interpret this predicted value.b)what is the predicted strength of a weld with a diameter of 51?
The equation of the least-squares line when y is expressed in kilograms is y = 2114.20 + 18.96x.
What is the linear system?
A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more two variables.
The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern.
Given the least square regression model equation:
y hat = -959.00 + 8.60x
weld diameter x ; shear strength y (in pounds)
1 lb = 0.4536 kg
To express shear strength y in kilogram:
y is multiplied by 0.4536
(y hat × 0.4536) = -959.00 + 8.60x
Divide both sides by 0.4536
(y hat × 0.4536) / 0.4536= (-959.00 + 8.60x) / 0.4536
y hat = 2114.1975 + 18.959435x
y hat = 2114.20 + 18.96x
The equation of the least-squares line when y is expressed in kilograms is y = 2114.20 + 18.96x.
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Disclaimer
The question given by you is incomplete, the above answer is done as per a similar question
The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern. The least-squares line is y hat = -959.00 + 8.60x. Because 1 lb = 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y = 0.4536(old y). What is the equation of the least-squares line when y is expressed in kilograms? (Give the answer to two decimal places.)
Solve the system of equations {y=15x+9y=12x−20.
What is the solution to the system?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system of equations is ( 160/11 , -100/37 )
The value of x = 160/111
The value of y = -100/37
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
y = 15x + 9y be equation (1)
y = 12x - 20 be equation (2)
Now , on simplifying the equations , we get
From equation (1) , we get
y = 15x + 9y
Subtracting y on both sides of the equations , we get
15x + 8y = 0
Subtracting 15x on both sides of the equations , we get
8y = -15x
Divide by 8 on both sides , we get
y = -15x/8 be equation (3)
Substitute the value of y from equation (3) in equation (2) , we get
12x - 20 = -15x/8
Multiply by 8 on both sides of the equation , we get
96x - 160 = -15x
Adding 15x on both sides of the equation , we get
111x - 160 = 0
Adding 160 on both sides , we get
111x = 160
Divide by 111 on both sides , we get
x = 160/111
Now , substitute the value of x in equation (3) , we get
y = -15x/8
y = ( -15 x 160 ) / ( 111 x 8 )
y = -100/37
Therefore , the value of x is 160/111 and value of y is -100/37
Hence , The solution to the system of equations is ( 160/11 , -100/37 )
The value of x = 160/111
The value of y = -100/37
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select a first-year college student at random and ask how many hours during a typical week did they spend studying or doing homework during their last year in high school? probabilities for the outcomes are time less than one hour 1 to 5 hours 6 to 10 hours more than 10 hours probability 0.1 0.5 0.2 0.2 to simulate the responses of randomly chosen first-year college students, how would you assign digits to represent the four possible outcomes listed?
The required probability for the students in given interval of time is answered below.
How we find probability by us probability distribution table?It lets you know probability for a specific score. To utilize one, initial transform your information into an ordinary dispersion. Then, at that point, find the matching z-score to one side of the table and adjust it to the z-score at the highest point of the table. The outcome gives you the probability.
According to question:By using table,
Probability study more than 10 hours = 1 - (.01+0.5+0.2)
⇒ 0.2
According to probability distribution table, if the sample of 10 students randomly,
1 student that less than one hour, 5 students whose study 1 to 5 hours, 2 students that study 6 to 10 hours, and 2 students that study more than 10 hours.
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y=3(x+7)-15 in standard form
Answer:
Step-by-step explanation:
ect the best answer for the question. 3. Rewrite the equation x + y + 3 = –2x + 4y + 18 into standard form (ax + by = c). A. 3x –3y = 5 B. x – y = 5 C. x – y = 15 D. x + y = 5
will this help?
The time it takes to read 10 pages of a book can be represented with the equation y equals 5.5 divided by 10 times x, where y represents the total time in minutes and x represents the number of pages read.
Determine how long it will take to read a book that has 305 pages.
105.5 minutes
167.75 minutes
305.89 minutes
554.55 minutes
Answer:
y = 554.55 minutes
Step-by-step explanation:
y = 5.5/10 x
y = 5.5/10 x 305
y = (5.5 x 305) / 10
y = 1677.5 / 10
y = 554.55 minutes
Answer:
It is given that:
The equation is:
y = (5.5/10)x
Here y represents the total time in minutes and x represents the number of pages read.
Plug x = 305
y = (5.5/10)(305)
y = 167.75 minutes
Thus, it will take 167.75 minutes to read a book that has 305 pages.
Option (B) 167.75 minutes is correct.f(x) = -(x)² over the x-axis 3 A) y=-x² how do u solve it on a graph
The graph is attached.
What is a quadratic equation?An equation with the highest power of the variable, 2, is considered to be a quadratic equation.
Given is a quadratic equation, y = -x²
Plotting the equation on graph,
When x = 1
y = -1²
y = -1
When x = 2
y = -2²
y = -4
When x = 3
y = -3²
y = -9
The points are;
(1,-1), (2, -4), (3, -9)
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Is 78 a multiple of 2? Explain your reasoning.
Answer:
Yes, 78 is a multiple of 2. A multiple of a number is a number that can be evenly divided by that number, and 78 can be evenly divided by 2. To prove this, we can perform the division: 78 / 2 = 39. Since there is no remainder when we divide 78 by 2, this means that 78 is a multiple of 2.
A video goes viral on social media, the number of views per day can be modeled with
the equation
y = -0.625x² + 5x
where x is the number of days after the video is posted and y is the number of views
per day in thousands. According to the model, after how many days do people stop
watching the video?
After 7 days, people will stop watching the video.
What is Substitution ?
The algebraic approach to solving simultaneous linear equations is known as substitution technique. In this process, the value of one variable from one equation is substituted in the second equation, as the name indicates.
We'll use the idea of substitution in this case.
The given equation is:-
y = -0.625x² + 5x
where x = number of days
y = number of views per day in thousands
Let's check, number of views on day 1
x=1
y = (-0.625×1²) + (5×1) = 4.375 => 4375 views
For day 2
x=2
y=(-0.625×2²)+(5×2) = 7.5 => 7500 views
For day 3
x=3
y=(-0.625×3²)+(5×3) = 9.375 => 9375 views
For day 4
x=4
y=(-0.625×4²)+(5×4) = 10 => 10000 views
For day 5
x=5
y=(-0.625×5²)+(5×5) = 9.375 => 9375 views
For day 6
x=6
y=(-0.625×6²)+(5×6) = 7.5 => 7500 views
For day 7
x=7
y = (-0.625×7²) + (5×7) = 4.375 => 4375 views
For day 8
x=8
y=(-0.625×8²)+(5×8) = 0 => 0 views
So, on day 8 there are 0 views, which means people will stop watching video after 7 days.
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From 8th day people will stop watching the video.
how many days do people stop watching the video?given:
y = -0.625x² + 5x
where x represents the number of days
y represents the no. of views per day.
solution:
for x=1
y = (-0.625) + (5)
= 4375
for x=2
y = (-0.62 5× 2² )+ (5 × 2 )
= 7500
for x=3
y=(-0.625 × 3² ) + ( 5 × 3 )
= 9375
for x=4
y=(-0.625 × 4² ) + ( 5 × 4 )
= 10000
for x=5
y=(-0.625 × 5² ) + ( 5 × 5 )
= 9375
For x=6
y=(-0.625 × 6² ) + ( 5 × 6 )
= 7500
For x=7
y = (-0.625 × 7² ) + ( 5 × 7 )
= 4375
For x=8
y=(-0.625 × 8²)+ ( 5 × 8 )
= 0
therefore from 8th day there will be 0 views on the video.
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Consider J.J.’s incomplete deposit slip:
How much cash did J.J. receive?
Responses
$22.25
$32.64
$100.00
$132.64
C.( $100.00) is the correct answer.
If you want to know how to get that answer, simply add all of the Cash and Checks together.
a popular word game starts with 100 letter tiles in a bag. the table shows the distribution for the vowels. vowel a e i o u number of tiles 9 12 9 8 4 on the first draw, one tile is selected. how many total outcomes are possible for this event?
The Probability of selecting a Vowel is 21/50
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Solution:
Adding the total number of Vowels = 9 + 12 + 9 + 8 + 4 = 42
Total Number of Letters = 100
Probability of getting a Vowel = 42/100
Probability = 21/50
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A snail travels at a rate of 31.68 in./min. find this rate in inches per second 
The snail travels at rate 0.528 in/sec.
What is rate?
A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
Given that,
A snail travels at a rate of 31.68 in./min.
This means
In 60 sec the snail travels 31.68 in.
In 1 sec the snail travels (31.68/60) in = 0.528 in.
This implies that the snail travels at rate 0.528 in/sec
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A lock ha a 3-number code made up of 26 number. If none of the number are allowed to repeat, how many different way can you chooe three different number in order for a unique code?
According to the given statement 15600 possible options to a unique code.
With examples, what are numbers?A digit is a numerical unit of measurement and labeling in mathematics. The real numbers 1, 2, 3, 4, and so on constitute the first instances.
Briefing:For the first password, we can choose any of the 26 numbers that are able, right? So for the first, we have 26 possible options.
For the second, we have 26 possible options minus 1 option which is already in use in the first password, so we have 26 -1 = 25 possible options here.
For the third, we also have 26 options, but we have to consider 2 unavailable options (1 in the first and 1 in the second), so we have 26 -2 = 24 options.
To finish it, we just have to multiply the possibilities of each lock:
26 * 25 * 24 = 15600 possible options to a unique code.
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